Sorafenib Tosylate With or Without Stereotactic Body Radiation Therapy in Treating Patients With Liver Cancer

Inclusion Criteria: * Patients must have a diagnosis of HCC by at least one criterion listed below within 360 days prior to study entry: * Pathologically (histologically or cytologically) proven diagnosis of HCC,(biopsies are recommended, and are to be submitted for research evaluation if patients consent) * At least one solid liver lesion or vascular tumor thrombosis (involving portal vein, inferior vena cava (IVC) and/or hepatic vein) \> 1 cm with arterial enhancement and delayed washout on multi-phasic computerized tomography (CT) or magnetic resonance imaging (MRI) in the setting of cirrhosis or chronic hepatitis B or C without cirrhosis. * For patients whose CURRENT disease is vascular only: enhancing vascular thrombosis (involving portal vein, IVC and/or hepatic vein) demonstrating early arterial enhancement and delayed washout on multi-phasic CT or MRI in a patient with known HCC (diagnosed previously \<720 days) using the above criteria. * Measureable hepatic disease and/or presence of vascular tumor thrombosis (involving portal vein, IVC and/or hepatic vein) which may not be measureable as per Response Evaluation Criteria in Solid Tumors (RECIST) on liver CT or MRI, within 28 days of registration * Appropriate for protocol entry based upon the following minimum diagnostic workup: * History/physical examination including examination for encephalopathy, ascites, weight, height, and blood pressure within 14 days prior to study entry * Assessment by radiatio…