Brief Summary: This phase II trial is studying how well AZD2171 works in treating patients with locally advanced unresectable or metastatic liver cancer. AZD2171 may stop the growth of tumor cells by blocking some of the enzymes needed for cell growth and by blocking blood flow to the tumor

Detailed Description: PRIMARY OBJECTIVE: I. Assess the progression free survival of patients with locally advanced unresectable or metastatic hepatocellular carcinoma treated with AZD2171. SECONDARY OBJECTIVES: I. Determine the toxicity of this drug in these patients. II. Determine, preliminarily, the efficacy of this drug, in terms of response rate, duration of response, and overall survival, in these patients. III. Determine the blood flow changes and vascular permeability of the tumor in patients treated with this drug. IV. Determine the pharmacokinetic profile of this drug in these patients. OUTLINE: This is a multicenter study. Patients receive oral AZD2171 once daily on days 1-28. Courses repeat every 28 days in the absence of disease progression or unacceptable toxicity. Dynamic contrast-enhanced (DCE) MRI and CT perfusion scan of the liver are performed at baseline, 72 hours after the initial dose of AZD2171, and at the end of course 1. Blood samples for pharmacokinetic studies are collected periodically during study. After the completion of study treatment, patients are followed every 3 months for 1 year.