Bevacizumab and Sorafenib in Treating Patients With Unresectable Stage III or Stage IV Malignant Melanoma

Criteria: * No substance abuse * Histologically or cytologically confirmed melanoma: * Unresectable (stage III) or metastatic (stage IV) disease * Measurable disease, defined as \>= 1 lesion that can be accurately and serially measured in \>= 1 dimension as \>= 20 mm with conventional techniques or as \>= 10 mm with spiral CT scan: * Cutaneous lesions measuring \>= 1 cm will be considered measurable disease * No primary ocular melanoma * No active CNS metastatic brain or meningeal tumors: * Prior CNS disease allowed provided it was definitely treated \>= 3 months ago AND there is no CNS disease by MRI or CT scan within the past 4 weeks * No residual disease * Life expectancy \> 12 weeks * ECOG performance status (PS) 0-2 OR Karnofsky PS 60-100% * WBC \>= 3,000/mm3 * Absolute neutrophil count \>= 1,500/mm3 * Platelet count \>= 100,000/mm3 * Bilirubin =\< 1.5 times upper limit of normal (ULN) * AST and ALT =\< 2.5 times ULN * Creatinine =\< 1.5 times ULN OR creatinine clearance \>= 60 mL/min * Serum amylase \< 1.5 times ULN OR lipase \< 1.5 times ULN * Urine protein:creatinine ratio \< 1.0 OR urine protein \< 1,000 mg by 24-hour urine collection * No significant traumatic injury in the past 28 days * Not pregnant or nursing * Negative pregnancy test * Fertile patients must use effective contraception during and for \>= 6 months after completion of study treatment * No history of allergic reactions attributed to compounds of similar chemical or biological composition to sorafenib tosylate and bevacizumab or other agents used in the study * No known hypersensitivity to Chinese hamster ovary cell products or other recombinant human antibodies * None of the following medical conditions: New York Heart Association class III-IV congestive heart failure; Cardiac arrhythmias, including atrial fibrillation if not adequately controlled; Active coronary artery disease or ischemia (e.g., unstable angina, cerebrovascular accident, transient ischemic attack, or myocardial infarction within the past 6 months); Uncontrolled hypertension * None of the following medical conditions: Clinically significant peripheral vascular disease; Evidence of bleeding diathesis or coagulopathy * No seizure disorder requiring medication (e.g., antiepileptics) * No prior or concurrent cancer that is distinct in primary site or histology from the cancer being evaluated except cervical carcinoma in situ, treated basal cell carcinoma, superficial bladder tumors (Ta, Tis, or T1) or any cancer treated with intent to cure, rather than for palliation, \< 3 years prior to study entry * No more than 2 prior immunotherapy, cytokine therapy, biologic therapy, or vaccine therapy regimens (e.g., aldesleukin) for advanced or metastatic disease: * (continued from above) Prior single-agent immunotherapy or combinations of immunotherapy as first treatment for advanced or metastatic disease allowed; Prior immunotherapy, cytokine therapy, biologic therapy, or vaccine therapy regimens in the adjuvant setting allowed * No immunotherapy, cytokine therapy, biologic therapy, or vaccine therapy (e.g., aldesleukin) for advanced or metastatic disease within the past 4 weeks * No prior organ allograft or stem cell transplantation * No prior Ras-pathway inhibitors (including trastuzumab \[Herceptin\], farnesyl transferase inhibitors, or MEK inhibitors) * No prior treatment with a drug that targets vascular endothelial growth factor (e.g., bevacizumab) * No prior thalidomide or sorafenib tosylate * No chemotherapy or radiotherapy within the past 4 weeks (6 weeks for nitrosoureas or mitomycin C) and recovered: Radiographic evidence of progression required for prior irradiated lesions * No major surgical procedure or open biopsy within the past 28 days * No Hypericum perforatum (St. John's wort) or rifampin within the past 3 weeks * Concurrent full-dose anticoagulants (e.g., warfarin) with PT INR \> 1.5 allowed provided the following criteria are met: Patient has an in-range INR (usually between 2 and 3) on a stable dose of oral anticoagulant or on a stable dose of low molecular weight heparin * AND (continued from above) Patient has no active bleeding or pathological condition that carries a high risk of bleeding (e.g., tumor involving major vessels or known varices) * No other concurrent investigational agents * No other concurrent anticancer agents or therapies * No concurrent carbamazepine, phenytoin, or phenobarbital (drugs that induce CYP450 3A activity) * No concurrent St. John's wort or rifampin * No concurrent radiotherapy * No concurrent major surgery * No history of or suspected HIV infection or clinically significant hepatitis B or C * No serious or nonhealing wound, ulcer, or bone fracture * No abdominal fistula, gastrointestinal perforation, or intra-abdominal abscess within the past 28 days * No active clinically serious infections * No dysphagia (difficulty swallowing) * No medical, psychological, or social condition that may preclude study participation or evaluation of the study results