Brief Summary: This phase II trial is studying how well sorafenib works in treating patients with metastatic, locally advanced, or recurrent sarcoma. 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. The primary endpoint is the response rate (CR+PR) for each stratum of sarcoma patients treated with sorafenib as defined by RECIST. SECONDARY OBJECTIVES: I. Progression-free survival (defined as CR + PR + SD, assessed at 3 months or 6 months). II. Overall survival. III. Pharmacokinetics of sorafenib in this patient population (all sites will participate). IV. Frequency of B-raf mutations in the patients' sarcomas treated as part of this study and correlation with response or resistance to sorafenib (all sites will participate). V. Ras-raf kinase pathway activation in pre-treatment existing tumor specimens (paraffin section immunohistochemistry; all sites will participate). VI. At MSKCC only: Pre and post treatment specimen changes in downstream events of ras signaling, specifically inhibition of ERK phosphorylation. Only patients with angiosarcoma and MPNST will undergo biopsy (up to 10 patients). VII. At MSKCC only: Circulating Endothelial Cells (CECs), VE-cadherin levels, and soluble protein levels (VEGF, bFGF, endostatin) as a measures of angiogenesis before and after starting sorafenib therapy. OUTLINE: This is an open-label, non-randomized, multicenter study. Patients are stratified according to sarcoma histology (angiosarcoma vs malignant peripheral nerve sheath tumor vs leiomyosarcoma \[closed to accrual as of 11/29/06\] vs high-grade undifferentiated pleomorphic sarcoma \[i.e., malignant fibrous histiocytoma (including myxofibrosarcoma)(closed to accrual as of 11/29/06)\] vs synovial sarcoma (closed to accrual as of 11/29/06) vs all other types of sarcoma). Patients receive oral sorafenib twice daily on days 1-28. Courses repeat every 28 days in the absence of disease progression or unacceptable toxicity. After completion of study, patients are followed at 4 weeks.