The main purpose of this study is to test the safety, tolerability, maximum tolerated dose, and effectiveness of bevacizumab in combination with chemotherapy and radiation therapy.

Because bevacizumab is not considered standard therapy for sarcomas, it can only be given to subjects with sarcoma who are enrolled in this research study and may only be administered under the direction of doctors who are investigators in this research study.

This study is being done because sarcomas can recur after surgical resection (surgery for removal of the tumor), radiation therapy and chemotherapy. This recurrence can occur in the same location as the original tumor or in distant sites such as the lung. Thus better treatments are needed.

This research study is a Phase I clinical trial. Phase I clinical trials test the safety of an investigational drug, combination of drugs, or combination of drugs with radiation. Phase I studies also try to define the appropriate dose of the investigational drug to use for further studies. "Investigational" means that the combination of drugs and radiation is still being studied and that research doctors are trying to find out more about it. It also means that the FDA has not approved bevacizumab with doxorubicin and radiation for your type of cancer.

In order to determine if patients are eligible for this study patients will undergo some screening procedures, including a medical history, physical examination, performance status, assessment of tumor, chest CT scan, blood tests, urine test, electrocardiogram and echocardiogram. Patients will also undergo blood tests and a tumor biopsy to look for markers for your particular type of cancer.

If it is determined that patients are eligible to be in the study they will need to have a central venous line (CVL), peripherally inserted central catheter (PICC), or portacath placement. Doxorubicin administration requires a central venous line, peripherally inserted central catheter (PICC) or portacath to be placed to allow continuous infusion of this drug.

Since the investigators are looking for the highest tolerable dose of the study drug, bevacizumab, that can be administered safely without severe or unmanageable side effects in participants that have sarcoma, not everyone who participates in this research study will receive the same dose of the study drug. The dose patients get will depend on the number of participants who have been enrolled in the study and how well they have tolerated their doses. The dose of doxorubicin and radiation therapy will be the same for all subjects throughout the study.

Bevacizumab will be given as an intravenous infusion (IV). The first infusion will take about 90 minutes. All other bevacizumab infusions will take either 60 or 30 minutes, if tolerated. The first infusion will be given on a Monday (excluding holidays). Patients will receive the second infusion 2 weeks later and then every 2 weeks after that for a total of 3 doses.

Doxorubicin will be given as an intravenous infusion (IV). It will be given through a port via an infusion pump about the size of a large wallet that can fit into a front-pack or "fanny-pack" around their waist. This pump will be connected to their body. The nurses in the infusion room will start the pump and disconnect it after 4 days. The first bolus infusion take will be given 1-2 hours after their first bevacizumab infusion and will take about 30 minutes. This will be followed by a continuous IV infusion of doxorubicin over 4 days. The first bolus infusion will be given on a Monday (excluding holidays) and the continuous infusion will go until Thursday. Patients will receive a second bolus infusion followed by a 4 day continuous infusion every week for 5 weeks.

Patients will begin radiation therapy after their first bevacizumab and doxorubicin infusion on Monday (excluding holidays). Radiation therapy will be delivered five days per week (Monday through Friday-excluding holidays) over a period of 6 weeks. This is done as an outpatient procedure. Each 2-week period will be considered a separate treatment cycle. Patients will be treated with radiation therapy for a maximum of 3 cycles (6 weeks).

The following tests and procedures will be done during the study during weeks 2, 4 and 6 and before surgery: a medical history, physical examination, performance status, blood tests, urine tests and assessment for any side effects. Patients will have additional CT scans of their chest and tumor before surgery. An ECG will be repeated at this time.

A surgeon will evaluate the tumor by reviewing radiologic studies before study treatment to determine if surgical removal is possible. After patients complete study treatment with radiation therapy and bevacizumab, a surgeon will repeat the evaluation of the tumor by reviewing radiologic studies to determine if surgical removal is still possible. Patients will have surgery 6-7 weeks after they finish radiation therapy.

Patients will have additional radiation therapy if the research doctor thinks that some cancer cells may have been left in their body in the area where the tumor was removed. The radiation may be given while patients are in surgery or about two weeks after the surgery. This will be determined by the surgeon and or radiation oncologist.

Patients will be in this research study for about 3 months. After the last dose of the study drug the investigators would like to keep track of their medical condition for 10 years. The investigators would like to do this by calling patients by telephone once a year to see how they are doing. Keeping in touch with them and checking their condition every year helps the investigators look at the long term effects of the research study.

Inclusion Criteria:

• Primary soft tissue sarcoma or isolated local recurrent sarcoma without prior radiation
• Histologically intermediate- or high-grade soft tissue sarcoma
• Determined by an expert sarcoma surgeon to have resectable disease located on the upper extremity, lower extremity, trunk, retroperitoneum or pelvis
• Primary tumor must be at least 5 cm in maximal diameter or an isolated local recurrence of any size

Exclusion Criteria:

• Metastatic disease
• Pregnant or breastfeeding
• Immunotherapy, chemotherapy, experimental therapy or radiotherapy within 4 weeks of first day of study drug dosing
• Previously received doxorubicin, any other anthracycline chemotherapy or bevacizumab
• Major surgery within 4 weeks before first day of study drug dosing
• Uncontrolled intercurrent illness
• History of myocardial infarction, acute coronary syndromes, coronary angioplasty or coronary artery stenting within previous 6 months
• Other medical or psychiatric conditions that may interfere with study participation
• Known hypercoagulable disorder
• Known history of deep vein thrombosis or pulmonary embolus
• Presence of bleeding diathesis or coagulopathy
• Current use of therapeutic anticoagulants