Gemcitabine and Docetaxel With Bevacizumab in Selected Sarcoma Subtypes

Inclusion Criteria: * Histologically confirmed unresectable metastatic or locally recurrent leiomyosarcoma, Malignant Fibrous Histiocytoma (MFH, also known as high grade Undifferentiated Pleomorphic Sarcoma) pleomorphic liposarcoma, rhabdomyosarcoma or angiosarcoma. * Zero to one prior chemotherapy regimens for metastatic disease. Prior adjuvant therapy will not count provided it was more than one year previously. * Measurable disease as defined by RECIST * Adequate performance status - ECOG 0 or 1 * Patients must be recovered from the toxic effects of prior chemotherapy or radiation. Therapy may not start until at least 3 weeks since prior cytotoxic chemotherapy, two weeks from completion of radiation therapy, and one week for patients on tyrosine kinase inhibitors or other targeted therapy. * Age 18 To 75. As it is quite difficult to administer high dose docetaxel with gemcitabine, to the elderly, in order to protect patient safety, we will restrict eligibility to patients between the ages of 18 and 75. * Adequate hematologic, hepatic and renal function as defined below * Hemoglobin \> or = to 8.0 g/dl * Absolute neutrophil count \> or = to 1,500/mm3 * Platelet count \> or = to 100,000/mm3 * Total Bilirubin \< or = to1.5 x upper limit of normal (ULN). * ALT (SGOT) or AST (SGPT) \< or = to 5 x ULN. * Alkaline Phosphatase \< or = to 2.5 x ULN or ≤ 5 x ULN in presence of liver metastases. * Serum creatinine 2.0 mg/dL * Ability to understand informed consent and comply with treatment protocol * Normal cardiac ejection fraction * Urine protein:creatinine (UPC) ratio \< than or = to 1.0 at screening Exclusion Criteria: * Uncontrolled intercurrent illness including infection or congestive heart failure within 6 months. * Prior therapy with gemcitabine, docetaxel or bevacizumab * Patients receiving other investigational agents * Patients with known brain metastases * Pregnancy or unwillingness to use effective birth control * Patients with HIV disease will be permitted, only if they are on effective anti-retroviral therapy, have a CD4 count greater than 400, and have had no opportunistic infections within the past 6 months. * Patients on anti-coagulation will be permitted if they are on a stable dose of warfarin or low-molecular weight heparin, and have had no major bleeds within the past 6 months. * Inability to comply with study and/or follow-up procedures. * Life expectancy of less than 12 weeks. * Current, recent (within 4 weeks of the first infusion of this study), or planned participation in an experimental drug study other than a Genentech-sponsored bevacizumab cancer study * Active malignancy, other than superficial basal cell and superficial squamous (skin) cell, or carcinoma in situ of the cervix within last three years * Inadequately controlled hypertension (defined as systolic blood pressure \> 150 and/or diastolic blood pressure \> 100 mmHg lasting \> 24 hours on antihypertensive medications) * Any prior history of hypertensive crisis or hypertensive encephalopathy * New York Heart Association (NYHA) Grade II or greater congestive heart failure * Significant vascular disease (e.g., aortic aneurysm, aortic dissection), requiring surgical repair or recent peripheral arterial thrombosis) within 6 months prior to Day 1 * Symptomatic peripheral vascular disease * Evidence of bleeding diathesis or significant coagulopathy (in the absence of therapeutic anticoagulation) * Major surgical procedure, open biopsy, or significant traumatic injury within 28 days prior to study enrollment or anticipation of need for major surgical procedure during the course of the study * Core biopsy or other minor surgical procedure, excluding placement of a vascular access device, within 7 days prior to study enrollment * History of abdominal fistula, gastrointestinal perforation, or intra-abdominal abscess within 6 months prior to study enrollment * Serious, non-healing wound, active ulcer, or non-healing bone fracture * Proteinuria at screening as demonstrated by * Urine protein:creatinine (UPC) ratio \> or = to 1.0 at screening (patients discovered to have UPC ratio \> or = to 1.0 at baseline should undergo a 24 hour urine collection and must demonstrate ≤ 1g of protein in 24 hours to be eligible). * Known hypersensitivity to any component of bevacizumab * Pregnant (positive pregnancy test) or lactating. Use of effective means of contraception (men and women) in subjects of child-bearing potential * History of hemoptysis (bright red blood of 1/2 teaspoon or more per episode) within 3 months prior to study enrollment. * Any history of stroke or transient ischemic attack within 6 months * History of myocardial infarction or unstable angina within 6 months