Sorafenib in Treating Patients With Metastatic or Recurrent Prostate Cancer

DISEASE CHARACTERISTICS: * Histologically confirmed adenocarcinoma of the prostate * Metastatic or recurrent disease * No curative standard therapy exists * Hormone-refractory disease * Evidence of prostate-specific antigen (PSA) progression during androgen ablation therapy, including medical or surgical castration * Documented PSA progression after completion of prior peripheral anti-androgens * At least a 25% increase (≥ 5 ng/mL) over a reference value PSA with 2 consecutive rising PSAs taken ≥ 1 week apart * Castrate level of testosterone ≤ 1.7 nmol/L for patients on medical androgen ablation * Patients receiving luteinizing hormone-releasing hormone agonist therapy must continue this treatment during study participation * PSA ≥ 10 ng/mL at the time of study entry * Primary tumor tissue (paraffin embedded) must be available for immunohistochemistry * Minimal symptomatic disease * No requirement for morphine or equivalent dose \> 30 mg/day to control pain * No known brain metastases PATIENT CHARACTERISTICS: Age * 18 and over Performance status * ECOG 0-1 Life expectancy * At least 12 weeks Hematopoietic * Absolute granulocyte count ≥ 1,500/mm\^3 * Platelet count ≥ 100,000/mm\^3 * No evidence of bleeding diathesis Hepatic * Bilirubin normal * AST and ALT ≤ 2.5 times upper limit of normal Renal * Serum creatinine normal OR * Creatinine clearance ≥ 60 mL/min Cardiovascular * No myocardial infarction within the past 6 months * No congestive heart failure * No unstable angina * No active cardiomyopathy * No unstable ventricular arrhythmia * No uncontrolled hypertension Other * No serious infection * No active peptic ulcer disease * No upper gastrointestinal or other condition that would preclude study compliance with oral medication * No uncontrolled psychotic disorder * No history of allergic reaction attributed to compounds of similar chemical or biologic composition to sorafenib or other study agents * No other serious illness or medical condition that would preclude study participation * No other malignancy within the past 5 years except adequately treated non-melanoma skin cancer or other curatively treated solid tumor PRIOR CONCURRENT THERAPY: Biologic therapy * Concurrent prophylactic filgrastim (G-CSF), sargramostim (GM-CSF), or other growth factors allowed for the management of adverse events only Chemotherapy * No prior chemotherapy * No other prior cytotoxic chemotherapy Endocrine therapy * See Disease Characteristics * Concurrent steroids allowed provided there has been no increase in steroid requirements within the past 4 weeks AND no increase in dose is planned Radiotherapy * At least 4 weeks since prior external-beam radiotherapy except low-dose non-myelosuppressive radiotherapy * Concurrent low-dose non-myelosuppressive palliative radiotherapy allowed Surgery * Not specified Other * No prior investigational anticancer agents * No concurrent therapeutic anticoagulation * Concurrent prophylactic low-dose warfarin for venous or arterial access devices allowed * No concurrent combination antiretroviral therapy for HIV-positive patients * No other concurrent anticancer therapy * No other concurrent investigational therapy * No concurrent grapefruit juice * Concurrent bisphosphonates allowed