The goal of this study is to find the highest tolerable dose of BAY 43-9006 (sorafenib) and bevacizumab that can be given with paclitaxel and carboplatin in patients with non-small cell lung cancer (NSCLC). The safety and effectiveness of this drug combination will also be studied.

Sorafenib is designed to stop the growth of cells that are caused by genetic changes often associated with cancer. Paclitaxel is designed to work by blocking the mechanisms of cell division in cancer cells, which may cause them to die. Carboplatin is designed to work by interfering with the growth of cancer cells by stopping cell division. Bevacizumab is designed to prevent or slow down the growth of cancer cells by blocking the effects of a blood-vessel stimulating agent that plays an important role in the growth of both normal and abnormal blood vessels.

If you are found to be eligible to take part in this study, you will receive 4 different drugs during the study. This study will follow a 3-week schedule known as a study "cycle."

In the first part of the study, researchers are trying to find out the highest dose of the study drugs that can be safely given together. The first group of 6 participants will receive lower doses of sorafenib and bevacizumab. The doses of paclitaxel and carboplatin will stay the same for up to 6 cycles for the study for all participants who complete 6 cycles. If the first 6 participants do not have intolerable side effects, the next group of patients will get higher doses of bevacizumab. The doses of sorafenib will be increased until at least some participants have unacceptable side effects. The dose that you get will not increase during the study, but if you have bad side effects, your dose of sorafenib, bevacizumab, paclitaxel, or carboplatin may be lowered at future visits.

On Day 1 of each cycle, you will be given bevacizumab, paclitaxel, and carboplatin in your vein as an infusion. Paclitaxel will be infused over 3 hours, followed by carboplatin over 30 minutes, followed by bevacizumab over 90 minutes for the first 2 cycles. Your bevacizumab infusion may be given over a shorter time period in later cycles. You will stay in the clinic for at least 30 minutes after your bevacizumab infusion for all cycles after 1 and 2. You will take sorafenib by mouth twice a day, once in the morning before 11:00 am and once in the evening before 11:00 p.m. Sorafenib should be taken with about 1 cup of water on an empty stomach (either 1 hour before a meal or 2 hours after a meal) or with a moderate fat diet (about 30% of calories from fat). Sorafenib must be swallowed whole without chewing.

On Day 1 of Cycles 1 and 2, your complete medical history will be recorded, and you will have a physical exam including measurement of your vital signs and weight. You will be asked questions to find out how the disease is progressing and how the disease affects the quality of life. You will be asked about any side effects you may be experiencing. If possible, you should not change your medications between Cycle 1 Day 1 until all procedures are completed on Cycle 2 Day 3. Blood (about 5 teaspoons) and urine will be collected for routine tests. You will receive infusions of paclitaxel, carboplatin, and bevacizumab into a vein.

On Cycle 1 Day 2, blood (about 1 tablespoon) will be drawn for routine tests.

On Cycle 1 Day 3, blood (about 1 tablespoon) will be collected for routine tests. After your blood samples have been collected, you will be given your morning dose of sorafenib. You will be given sorafenib to take at home that night.

On Cycle 2 Day 2, blood (about 1 tablespoon) will be drawn for routine tests. Once your blood samples has been collected, your morning dose of sorafenib will be given to you in the clinic. You will be given sorafenib to take at home that night.

On Cycle 2 Day 3, blood (about 1 tablespoon) will be drawn for routine tests. Once your blood sample has been collected, your morning dose of sorafenib will be given to you in the clinic. Before you leave the clinic, you will be given enough sorafenib tablets to last until your next cycle visit.

On Cycles 1-2 Days 8 and 15, your complete medical history will be recorded, and you will have a physical exam including measurement of your vital signs and weight. You will have a performance status evaluation. You will be asked about any side effects you may be experiencing. Blood (about 5 teaspoons) and urine will be collected for routine tests.

On Day 1 of Cycle 3 and remaining cycles, you will return all study medication and/or the empty bottle. Your complete medical history will be recorded, and you will have a physical exam including measurement of your vital signs and weight. You will be asked questions to determine how the disease is progressing, and how the disease affects your quality of life. You will be asked about any side effects you may be experiencing. Blood (about 5 teaspoons) and urine will be collected for routine tests. You will receive infusions of paclitaxel, carboplatin, and bevacizumab. You will stay in the clinic for at least 30 minutes after your bevacizumab infusion. Before you leave the clinic, you will be given enough sorafenib to last until the next cycle.

On Days 8 and 15 of Cycle 3 and remaining cycles, blood (about 5 teaspoons) and urine will be collected for routine tests.

On Day 1 of all odd-numbered cycles (starting with Cycle 3, 5, 7, 9...), you will have CT scans, MRI scans, and/or other x-rays to check the status of the disease.

Modified Dose Levels 4 and 5:

To find out if interrupted dosing of sorafenib will result in fewer or less severe side effects, 2 additional dose levels, where the dose of sorafenib will be changed (modified), will be performed. For Modified Dose Level 4, sorafenib will be interrupted for 2 days after every 4-5 days . For Modified Dose Level 5, sorafenib will be interrupted for 1 week after 2 weeks of continuous therapy.

For these 2 additional dose levels, the sorafenib dosing schedule will be changed. There will be 6 patients enrolled at each dose level. Participants in Dose Level 4 may continue treatment for 4 to 6 cycles. This is done to accurately evaluate the dose level. Researchers will evaluate any side effects related to this new dosing schedule of sorafenib. After all 6 patients have been enrolled in Dose level 4, then 6 additional patients will be enrolled in Dose Level 5. If no intolerable side effects are seen at Dose Level 5, then 6 additional patients can be enrolled in that dose level. This is done so additional PK testing can be done.

For Modified Dose Level 4 and 5, "on Day 1 of Cycle 1 and 2, you will be given bevacizumab, paclitaxel, and carboplatin in your vein as an infusion. Paclitaxel will be infused over 3 hours, followed by carboplatin over 30 minutes, followed by bevacizumab over 90 minutes for the first 2 cycles. Your bevacizumab infusion may be given over a shorter time period in later cycles. You will stay in the clinic for at least 30 minutes after your bevacizumab infusion for all cycles after 1 and 2. "

Modified Dose level 4:

For Modified Dose level 4, on Day 3 through Day 19 of Cycle 1, you will receive sorafenib by mouth in the morning, after the morning PK tests have been collected (on Day 3 only). Participants will take the evening dose of sorafenib on their own. After that, participants will take sorafenib on their own twice a day for 5 days on and 2 days off. This will continue through Day 19 on an outpatient basis.

On Day 2 through Day 19 of Cycle 2, you will receive sorafenib by mouth in the morning, after the morning PK tests have been collected on Day 2 (Cycle 2 only). Participants will take the evening dose of sorafenib on their own. After that, participants will take sorafenib on their own twice a day for 5 days on and 2 days off. This will continue through Day 19 on an outpatient basis. The modified dose level 4 and 5 patients will not take sorafenib on Days 1, 2, 6, 7, 13, 14, 20 and 21 of Cycle 1.

Modified Dose level 5:

For Modified Dose Level 5, on Day 3 through Day 15 of Cycle 1, you will receive sorafenib by mouth in the morning, after the morning PK tests have been collected (on Day 3 only). Participants will take the evening dose of sorafenib on their own. After that, participants will take sorafenib on their own twice a day for 14 days through Day 15 on an outpatient basis. Participants will not take sorafenib on Days 1, 2 and Days 16-21.

On Day 2 through Day 15 of Cycle 2, you will receive sorafenib by mouth in the morning, after the morning PK tests have been collected (on Day 2 Cycle 2 only). Participants will take the evening dose of sorafenib on their own. After that, participants will take sorafenib on their own twice a day for 14 days through Day 15 on an outpatient basis.Participants will not take sorafenib on Days 1, 2 and Days 16-21.

You may stay on study as long as the disease does not get worse, and intolerable side effects do not develop.

Once you are off study, you will have an end-of-study visit 21-35 days after your last dose of the study drug. You will need to return all unused study medication and/or the empty bottles. You will have a physical exam, including measurement of your vital signs, height, and weight. You will have a performance status evaluation and an ECG. You will be asked about any side effects you may be experiencing. CT scans, MRIs, and/or x-rays will be taken to check the status of the disease. Blood (about 5 teaspoons) and urine will be collected for routine blood tests. Women who are able to have children must have a negative blood (about 1-2 teaspoons ) pregnancy test.

This is an investigational study. Sorafenib, paclitaxel, carboplatin, and bevacizumab are all FDA approved and commercially available. The combination of these 4 drugs is not FDA approved, and it has been authorized for use in research only. Up to 60 patients will take part in this multicenter study. Up to 30 patients will be enrolled at M.D. Anderson.

Inclusion Criteria:

1. Ability to understand and the willingness to sign a written informed consent. A signed informed consent must be obtained prior to any study specific procedures.
2. Patients must have Stage IIIB (with malignant pleural effusions) or Stage IV histological or cytological confirmation of non-small cell carcinoma (excluding squamous).
3. Age >/= 18 years old
4. Patients must have at least 1 measurable lesion. Lesions must be evaluated by computed tomography (CT) scan or magnetic resonance imagining (MRI)
5. Eastern Cooperative Oncology (ECOG) Performance Status of 0 - 1
6. Controlled blood pressure (defined as systolic BP </= 150mmHg and diastolic </= 90 mmHg)
7. Adequate bone marrow, liver and renal function as assessed by the following laboratory requirements to be conducted within 7 days prior to start of first dose: Hemoglobin >/= 9.0 g/dL; White blood cell (WBC) count >/= 2,500/mm3, Absolute neutrophil count (ANC) >/= 1,500/mm3, Platelet count >/= 100,000/mm3, Total bilirubin </= 1.5 times the upper limit of normal (ULN), ALT and AST </= 2.5 x ULN (</=5 x ULN for patients with liver involvement), international normalized ratio (INR) </= 1.5 and activated partial thromboplastin time (aPTT) within normal limits.
8. Inclusion Criteria #7: Serum creatinine </= ULN or creatinine clearance (CrCl) >/= 45 mL/min (CrCl = Wt (kg) x (140 - age)/72 x Cr level, female x 0.85) for patients with creatinine levels above institutional normal. Urinalysis (UA) must show less than 1+ protein urine, or the patient will require a repeat UA. If repeat UA shows 1+ protein or more, a 24 hour collection will be required and must show total protein </= 1000 mg/24 hour to be eligible
9. Women of childbearing potential must have a negative serum pregnancy test performed within 7 days prior to start of treatment.
10. Women of childbearing potential and men must agree to use adequate contraception prior to study entry and for the duration of study participation, including the 30 day period after last study drug dosing. The investigator should advise the patient what is considered adequate contraception.

Exclusion Criteria:

1. Patients with squamous histology.
2. Cardiac disease: Congestive heart failure (CHF) > Class II New York Heart Association (NYHA); active coronary artery disease (myocardial infarction) [MI] more than 6 months prior to study entry is allowed); or serious cardiac ventricular arrhythmias requiring anti-arrhythmic therapy (beta-blockers or digoxin are permitted)
3. Uncontrolled hypertension defined as systolic blood pressure > 150 mmHg or diastolic pressure > 90 mmHg despite optimal medical management
4. Human Immunodeficiency Virus (HIV) infection or chronic hepatitis B or C
5. Active clinically serious infections (> Grade 2 NCI-CTC Version 3.0)
6. History of brain metastases. Patients with history of brain metastases are eligible as long as the metastasis has been treated with either stereotactic whole brain radiation or neurosurgery, patient does not require ongoing treatment with dexamethasone and patient's radiographic imaging is stable >/= 4 weeks from start of treatment. Time from brain metastasis treatment to first study treatment must meet the following criteria: Stereotactic whole brain radiation >/= 4 weeks from first study treatment, Neurosurgery >/= 24 weeks from first study treatment, continued in exclusion # 7
7. Continued from exclusion criterion # 6: Brain biopsy >/= 12 weeks from first study treatment.
8. Uncontrolled seizure disorder. Use of cytochrome P450 enzyme-inducing antiepileptic drugs (phenytoin, carbamazepine or phenobarbital) is not allowed
9. Thrombotic or embolic events such as cerebrovascular accident, transient ischemic attacks, deep vein thrombosis or pulmonary embolism
10. Organ allograft
11. Evidence or history of bleeding diathesis or coagulopathy
12. History of/or current evidence of hemoptysis (bright red blood of 1/2 teaspoon or more)
13. Peripheral neuropathy >/= Grade 2
14. Anticancer chemotherapy or immunotherapy: Anticancer therapy is defined as any agent or combination of agents with clinically proven anticancer activity administered by any route with the purpose of affecting the cancer, either directly or indirectly, including palliative and therapeutic endpoints (except patients who have received adjuvant chemotherapy > 52 weeks from Cycle 1 Day 1)
15. Radiotherapy to the target lesions within 3 weeks of start of first dose. Toxicities from radiotherapy must have resolved prior to start of first dose.
16. No major surgery, open biopsy or significant traumatic injury within 4 weeks of start of first dose
17. Serious, non-healing wound, ulcer, or bone fracture
18. Granulocyte growth factors (G-CSF), within 3 weeks of study entry.
19. Patients taking chronic erythropoietin are permitted provided no dose adjustment is made within 2 months prior to start of first dose
20. Pregnant or breast feeding patients
21. Substance abuse, medical, psychological or social conditions that may interfere with the patient's participation in the study or evaluation of the study results
22. Known or suspected allergy to any recombinant human antibodies, or compounds of similar chemical or biologic composition to sorafenib or any of the drugs in this study
23. Any condition that is unstable or could jeopardize the safety or compliance of the patient in the study
24. Previous or concurrent cancer that is distinct in primary site or histology from the cancer being evaluated in the study EXCEPT cervical cancer in situ, treated basal cell carcinoma, superficial bladder tumors (Ta, Tis, and T1) or any cancer curatively treated > 3 years prior to study entry
25. Any condition that impairs the patient's ability to swallow pills as a whole
26. Any malabsorption conditions
27. Therapeutic anticoagulation with warfarin, heparins, or heparinoids
28. Patients takin phenytoin, carbamazepine, and Phenobarbital
29. Patients taking rifampin, St. John's Wort