 This is an investigational study. Both cisplatin and pemetrexed have been approved by the FDA for the treatment of malignant mesothelioma. The FDA has approved imatinib mesylate for the treatment of leukemia and certain sarcomas; however, it has been authorized by the FDA for use in research only in the treatment of malignant mesothelioma. Up to 42 patients will take part in this study. All will be enrolled at M. D. Anderson. 