You are being asked to take part in this study because you have multiple myeloma that has either not responded to therapy (resistant), or did respond to therapy and has now come back (relapsed).  The purpose of this study is to find out what the effects are (good and bad) of treatment with BAY 43-9006 (Sorafenib) for resistant or relapsed multiple myeloma.  Your participation in this study is expected to last for at least one cycle (28 days) of treatment with BAY 43-9006, but may continue indefinitely, unless your myeloma shows signs of worsening, or you develop side effects, which in the opinion of you and your doctor, make it necessary to discontinue the medication.  After you are finished with your treatment, you will be followed for approximately 5 years. 

You are also being asked to take part in a research specimen study because you have multiple myeloma and are participating in the treatment part of this study.  The purpose of this study is to collect additional specimens to be stored for future studies. To perform biologic studies on samples from groups of patients with the same disease who have been treated in a uniform way, the Southwest Oncology Group (SWOG) has created a tissue bank to collect these specimens.  These tissue samples will be used to generate scientific information to assist in the development of treatments for multiple myeloma.  Your participation in this study is expected to last for the length of time required for the blood draw and bone marrow aspiration—approximately 10 minutes at two time points: prior to treatment and when your disease returns.