This phase II trial is studying how well giving bevacizumab together with sorafenib works in treating patients with unresectable stage III or stage IV malignant melanoma. Monoclonal antibodies, such as bevacizumab, can block tumor growth in different ways. Some block the ability of tumor cells to grow and spread. Others find tumor cells and help kill them or carry tumor-killing substances to them. Sorafenib may stop the growth of tumor cells by blocking some of the enzymes needed for cell growth. Bevacizumab and sorafenib may also stop the growth of melanoma by blocking blood flow to the tumor. Giving bevacizumab together with sorafenib may kill more tumor cells.