This randomized phase III trial studies sorafenib tosylate and stereotactic body radiation therapy to see how well they work compared to sorafenib tosylate alone in treating patients with liver cancer. Sorafenib tosylate may stop the growth of tumor cells by blocking some of the enzymes needed for cell growth. Stereotactic body radiation therapy may be able to send the radiation dose directly to the tumor and cause less damage to normal tissue. Giving sorafenib tosylate together with stereotactic body radiation therapy may kill more tumor cells.