Brief Summary: This phase II trial is studying how well sorafenib works in treating patients with progressive regional or metastatic cancer of the urothelium. Sorafenib 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 OBJECTIVES: I. To evaluate the 4-month progression-free survival rate, response rate and toxicity of BAY 43-9006 in patients with progressing regional or metastatic transitional cell carcinoma (or mixed histologies containing a component of TCC) of the urothelium who have progressed on one and only one prior systemic chemotherapy regimen for metastatic disease. SECONDARY OBJECTIVES: I. To determine the time to disease progression and overall survival with BAY 43-9006. II. To evaluate the frequency of polymorphisms in drug metabolizing enzymes and to correlate these polymorphisms with variations in BAY 43-9006 pharmacokinetics. III. To evaluate the frequency of raf kinase mutations in tumor specimens and correlate these with response rate. IV. To evaluate serum VEGF levels as potential markers of angiogenesis inhibition by BAY 43-9006. V. To evaluate markers of apoptosis and kinase inhibition in peripheral blood mononuclear cells as potential biomarkers of BAY 43-9006 activity. VI. To determine if there are proteins differentially translated from the genome in patients who respond to treatment with BAY 43-9006 versus patients who do not respond to BAY 43-9006. OUTLINE: This is a multicenter study. Patients receive oral sorafenib twice daily on days 1-56. Courses repeat every 56 days in the absence of disease progression or unacceptable toxicity. After completion of study treatment, patients are followed every 3 months until 2 years from study entry and then every 6 months until 3 years from study entry.