Sorafenib Tosylate in Treating Patients With Malignant Mesothelioma.

Inclusion Criteria: * Histologically documented malignant mesothelioma, epithelial, sarcomatoid or mixed type, not amenable to curative surgery; any site of origin of malignant mesothelioma, including but not limited to: pleura, peritoneum, pericardium and tunica vaginalis is allowed * Pathology blocks or slides from a core surgical biopsy must be available for evaluation of ERK 1/2 phosphorylation by immunohistochemistry and for sequencing of B-raf exons 11 and 15 * Chemotherapy naive or no more than one pemetrexed containing chemotherapy regimen; chemotherapy may have been pemetrexed alone or in combination with any other agent * No prior tyrosine kinase/signal transduction/angiogenesis inhibitor therapy * Prior intracavitary cytotoxic or sclerosing therapy (including bleomycin) are acceptable; prior intrapleural cytotoxic chemotherapy will not be considered systemic chemotherapy * \>= 3 weeks since major surgery * \>= 4 weeks since completion of prior radiation therapy, as long as measurable disease lies outside of the radiation port * \>= 4 weeks since the completion of prior pemetrexed-containing chemotherapy * No treatment with an investigational agent currently or within the last 28 days * No patients with known brain metastases; 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 the evaluation of neurologic and other adverse events * Patients with pleural rind only disease must have at least one level with one rind measurement \>= 1.5 cm * Measurable disease is defined as lesions that can be accurately measured in at least one dimension (longest diameter to be recorded) as \>= 20 mm with conventional techniques (CT, MRI, x-ray) or as \>= 10 mm with spiral CT scan * ECOG Performance status of 0-1 * No prior history of allergic reactions attributed to compounds of similar chemical or biologic composition to BAY 43-9006 * Non-pregnant and non-nursing because the effects of BAY 43-9006 on the fetus/infant are unknown; in addition, women of child-bearing potential and men must agree to use an appropriate method of birth control throughout their participation in this study; appropriate methods of birth control include abstinence, oral contraceptives, implantable hormonal contraceptives (Norplant), or double barrier methods (diaphragm plus condom) * Patients with a "currently active" second malignancy other than non melanoma skin cancers and carcinoma in situ of the cervix are not eligible; patients are not considered to have a "currently active" second malignancy if they have completed therapy and are considered to have a less than 30% chance of risk of relapse * No patients with uncontrolled intercurrent illness including but not limited to: ongoing active infections, symptomatic congestive heart failure, unstable angina pectoris, hypertension, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements * No patients on therapeutic anticoagulation; prophylactic anticoagulation (i.e., low dose warfarin) of venous or arterial access devices is allowed provided that the requirements for INR are met * No evidence of bleeding diathesis * No HIV positive patients receiving combination anti-retroviral therapy; 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 because of possible pharmacokinetic interactions with BAY 43-9006 * Granulocytes \>= 1,500/ul * Platelet count \>= 100,000/μl * Total Bilirubin =\< 1.5 x ULN * AST (SGOT) =\< 2.5 x ULN * Creatinine or Creatinine Clearance =\< 1.5 x ULN \>= 60 ml/minute * INR \< 1.5