Sorafenib in Treating Patients With Advanced or Metastatic Cancer of the Urinary Tract

Inclusion Criteria: * Patients must have histologically or cytologically confirmed transitional cell cancer of the bladder, renal pelvis or ureter * Patients must have measurable disease, defined as at least one lesion that can be accurately measured in at least one dimension (longest diameter to be recorded) as \>= 20 mm with conventional techniques or as \>= 10 mm with spiral CT scan * Patients must not have had any prior systemic therapy for advanced or metastatic disease; prior adjuvant or neoadjuvant chemotherapy is permitted providing it was completed at least 4 weeks prior to study entry; radiation therapy is permitted if completed \> 4 weeks prior to trial entry * Life expectancy of greater than 3 months * ECOG performance status 0 or 1 (Karnofsky \>= 70%) * Leukocytes \>= 3,000/uL * Absolute neutrophil count \>= 1,500/uL * Platelets \>= 100,000/uL * Total bilirubin within normal institutional limits * AST(SGOT)/ALT(SGPT) =\< 2.5 X institutional upper limit of normal * Creatinine \< 1.5 x ULN OR creatinine clearance \>= 45 mL/min/1.73 m\^2 * No serious medical conditions such as myocardial infarction within 6 months prior to entry, congestive heart failure, unstable angina, active cardiomyopathy, unstable ventricular arrhythmia, uncontrolled hypertension, uncontrolled psychotic disorders, serious infections, active peptic ulcer disease, or any other medical conditions that might be aggravated by treatment * Patients must have tumor lesions accessible for biopsy for correlative studies and must be willing to undergo tumor biopsy once before and once during experimental therapy; if there is a medical contraindication to biopsy, exception may be granted upon discussion with the Principal Investigator/Chair * Women of child-bearing potential and men must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to study entry and for the duration of study participation; should a woman become pregnant or suspect she is pregnant while participating in this study, she should inform her treating physician immediately * Able to swallow and retain oral medication * Ability to understand and the willingness to sign a written informed consent document Exclusion Criteria: * Prior systemic therapy for advanced or metastatic urothelial carcinoma * Patients who have had chemotherapy or radiotherapy within 4 weeks (6 weeks for nitrosoureas or mitomycin C) prior to entering the study or those who have not recovered from adverse events due to agents * Patients receiving any other investigational agents, or concurrent anticancer therapy * Patients with only non-measurable disease, defined as all other lesions, including small lesions (longest diameter \< 20mm with conventional techniques or \< 10 mm with spiral CT scan) and truly non-measurable lesions, which include the following: * Bone lesions * Leptomeningeal disease * Ascites * Pleural/pericardial effusion * Inflammatory breast disease * Lymphangitis cutis/pulmonis * Abdominal masses that are not confirmed and followed by imaging techniques * Cystic lesions * Patients with known brain metastases should be excluded from this clinical trial because of their poor prognosis and because they often develop progressive neurologic dysfunction that would confound evaluation of neurologic and other adverse events * Patients with a history of other active malignancy in the past 5 years (with the exception of adequately treated cervical carcinoma in situ and non melanomatous skin cancers) are excluded * Uncontrolled intercurrent illness including, but no limited to, ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements * Patients must not have any evidence of a bleeding diathesis * Patients must not be on therapeutic anticoagulation; prophylactic anticoagulation (ie. Low dose warfarin) of venous or arterial access devices is allowed provided that the requirements for PT, INR or PTT are met * Patients must not be taking the cytochrome P450 enzyme-inducing antiepileptic drugs (phenytoin, carbamazepine, or Phenobarbital), rifampin or St. John's Wort * Pregnant women are excluded from this study; breastfeeding should be discontinued if the mother is treated with BAY 43-9006 * Patients with immune deficiency are at increased risk of lethal infections when treated with marrow-suppressive therapy; therefore, HIV-positive patients receiving combination anti-retroviral therapy are excluded from the study * History of allergic reactions attributed to compounds of similar chemical or biologic composition to BAY 43-9006 * Patients with GI tract disease resulting in an inability to take oral medication, malabsorption syndrome, a requirement for IV alimentation, prior surgical procedures affecting absorption, uncontrolled inflammatory GI disease (e.g., Crohn's, ulcerative colitis)