The main purpose of this study is to find the maximum tolerable dose of sorafenib when administered along with another drug called 5-Fluorouracil (5-FU) and to find out more about whether these drugs, along with radiation, can help people with rectal cancer when given before surgery. 5-FU and radiation are both approved by the US Food and Drug Administration (FDA) for use in people with rectal cancer.

The investigators will utilize a standard 3 + 3 phase I study design. In the phase I part of the study, the investigators will attempt dose escalation of sorafenib in combination with standard infusional 5-FU and external beam at standard doses. Clinical staging should be done by endorectal ultrasound (ERUS) and/or pelvic magnetic resonance imaging (MRI) for T and N stage; chest and abdomen computed tomography (CT) for staging of metastatic disease; undergo sigmoidoscopy and/or colonoscopy done by crude odds ratios (CORS); biopsy is taken for diagnosis and extra is sent for tissue bank. At the maximum tolerated dose (MTD) of sorafenib we will expand the cohort to 6 more patients to further evaluate toxicity profile and efficacy.

Participants' study regimen will include 5 ½ weeks of radiation. Radiation sessions will be daily, Monday through Friday, except for holidays. 5-FU will be delivered at a dose of 225 mg/m² daily through a catheter in a large vein continuously until the last day of radiation. In addition, sorafenib will be taken by mouth twice daily every day until the last day of radiation. The dose of sorafenib participants may receive will be one of the following: 200 mg every other day, 200 mg daily, 400 mg daily, or 800 mg daily. Following completion of this phase of the study, participants will receive no study drug or radiation for one month. At 4 to 5 weeks after stopping study drug and radiation, participants will have another CT scan or MRI to assess their cancer. About 6 to 8 weeks after the end of radiation, participants will undergo surgery and every effort will be made to remove the tumor. The surgery will occur just as it would if participants were not in the study, except that a portion of their tumor obtained during surgery will be used for research biomarker testing (as described in the consent form).

Approximately 6 -10 weeks after participants' surgery, when they have adequately healed, they may receive additional chemotherapy at their study doctor's discretion.

Inclusion Criteria:

• Histologically confirmed adenocarcinoma of the rectum that begins within 12 cm of the anal verge as determined by sigmoidoscopy and/or colonoscopy with no evidence of distant metastasis
• Locally advanced rectal cancer determined by any of the following features: Fixed or immobile tumor on physical exam and/or; T3 disease with invasion through the muscularis propria as defined by transrectal ultrasound, CT or MRI; T4 disease with invasion of adjacent structures such as pelvic sidewall, sacrum, pelvis, bladder and/or prostate as determined appropriate imaging modalities such as ultrasound, CT or MRI; Any T with + N on CT scan/MRI or transrectal ultrasound
• Eastern Cooperative Oncology Group (ECOG) Performance Status 0 or 1
• Adequate bone marrow, liver and renal function as assessed by the following: Hemoglobin > 9.0 g/dl, Absolute neutrophil count (ANC) > 1,500/mm^3, Platelet count > 100,000/mm^3, Total bilirubin < 1.5 times upper limit of normal (ULN), alanine aminotransferase (ALT) and aspartate aminotransferase (AST) < 2.5 times the ULN ( < 5 x ULN for patients with liver involvement), Creatinine < 1.5 times ULN
• Women of childbearing potential must have a negative serum pregnancy test performed within 7 days prior to the start of treatment
• Women of childbearing potential and men must agree to use adequate contraception (barrier method of birth control) prior to study entry and for the duration of study participation. Men should use adequate birth control for at least three months after the last administration of sorafenib.
• 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.
• Patients receiving anti-coagulation treatment with an agent such as warfarin or heparin will be allowed to participate. For patients on warfarin, the INR should be measured prior to initiation of sorafenib and monitored at least weekly, or as defined by the local standard of care, until international normalized ratio (INR) is stable.

Exclusion Criteria:

• Cardiac disease: Congestive heart failure > class II New York Heart Association (NYHA). Patients must not have unstable angina (anginal symptoms at rest) or new onset angina (began within the last 3 months) or myocardial infarction within the past 6 months.
• Pelvic irradiation therapy.
• Cardiac ventricular arrhythmias requiring anti-arrhythmic therapy.
• Uncontrolled hypertension defined as systolic blood pressure > 150 mmHg or diastolic pressure > 90 mmHg, despite optimal medical management.
• Known human immunodeficiency virus (HIV) infection or chronic Hepatitis B or C.
• Active clinically serious infection > Common Terminology Criteria for Adverse Events (CTCAE) Grade 2.
• Thrombolic or embolic events such as a cerebrovascular accident including transient ischemic, attacks, deep vein thrombosis (DVT) within the past 6 months.
• No active malignancy except for nonmelanoma skin cancer or in situ cervical cancer or Treated non-pelvic cancer from which the patient has been continuously disease free more than five years.
• Needing medical attention for serious bleeding in past 4 weeks.
• Previous chemotherapy except for antiangiogenic agent or tyrosine kinase inhibitor (TKI) will be allowed as long as it is more than 5 years.
• Evidence or history of bleeding diathesis
• Use of St. John's Wort or rifampin
• Known or suspected allergy to sorafenib or any agent given in the course of this trial.
• Any condition that impairs patient's ability to swallow whole pills.
• Any malabsorption problem.