Patients receive oral sorafenib tosylate on days 1-5, 8-12, 15-19, and 22-26 and bevacizumab IV over 30-90 minutes on days 1 and 15. Treatment repeats every 28 days in the absence of unacceptable toxicity or disease progression. Blood samples and tumor biopsies are obtained periodically for pharmacokinetic and pharmacodynamic studies. Samples are examined by liquid chromatography, mass spectrometry, immunohistochemistry, gene expression analysis, DNA mutation analysis, and genomic analysis for biological markers.