This is an investigational study. Imatinib Mesylate has been approved for chronic myelogenous leukemia patients. However this is an investigational study of Imatinib Mesylate in patients with ovarian, tubal, or peritoneal cancer. Participants may responsible for the cost of all or part of this drug. At least 24 and as many as 74 patients will take part in this study. All will be enrolled at M. D. Anderson.