This phase I/II trial studies the side effects and best dose of sorafenib tosylate and bevacizumab and to see how well they work in treating patients with advanced kidney cancer. Sorafenib tosylate may stop the growth of tumor cells by blocking some of the enzymes needed for cell growth. Monoclonal antibodies, such as bevacizumab, can block tumor growth by targeting certain cells. Bevacizumab and sorafenib tosylate may also stop the growth of tumor cells by blocking blood flow to the tumor. Giving sorafenib tosylate together with bevacizumab may kill more tumor cells.