• To find the highest tolerable dose of the drug combination (cisplatin, pemetrexed [Alimta®], and imatinib mesylate [Gleevec®]) that can be given to patients with unresectable or metastatic malignant mesothelioma. [ Time Frame: 2 Years ] [ Designated as safety issue: No ]
  

• The safety and effectiveness of this treatment combination will also be studied. [ Time Frame: 2 Years ] [ Designated as safety issue: Yes ]
  

Inclusion Criteria:

• A written, voluntary informed consent form must be completed prior to beginning any study procedure.
• Patients >/= 18 years of age.
• Histologically documented diagnosis of malignant mesothelioma.
• Performance status 0-2 (ECOG)
• Pts must have adequate hepatic,renal,& bone marrow function,defined as the following:(1) total bilirubin </=1.5xULN;(2) SGOT & SGPT</=2.5xULN;(3)creatinine </= 1.5xULN;(4) ANC >/= 1.5x10^9/L;(5) platelets>/=100 x 10^9/L.Note:Renal function is only based on serum creatinine level </= 1.5xULN.The standard Cockcroft & Gault formula or the measured glomerular filtration rate (GFR) using the appropriate radiolabelled method (51-CrEDTA or Tc99m-DTPA) must be used to calculate CrCl for enrollment or dosing.The same method used @ baseline should be used throughout the study.CrCl should be >/= 45mg/dl.
• Female patients of childbearing potential must have negative pregnancy test within 7 days before initiation of study drug dosing. Postmenopausal women must be amenorrheic for at least 12 months to be considered of non-childbearing potential. Male and female patients of reproductive potential must agree to employ an effective barrier method of birth control throughout the study and for up to 3 months following discontinuation of study drug.
• Patients who have not received prior chemotherapy for their metastatic or recurrent unresectable malignant mesothelioma; with the exception of patients who have recurrent mesothelioma after induction chemotherapy followed by definitive treatment (surgery +/- radiotherapy). Patients must have had 2 or fewer cycles/doses of induction chemotherapy and must have had tumor response to the induction therapy.
• Patients must have documented unresectable malignant mesothelioma (pleural or peritoneal).
• Patients with treated brain metastasis who have stable brain disease (i.e. no steroids at least 4 weeks prior to study enrollment).

Exclusion Criteria:

• Patient has received any other investigational agents within 28 days of first day of study drug dosing.
• Patient is </= 5 years free of another primary malignancy except: if the other primary malignancy is not currently clinically significant nor requiring active intervention, or if other primary malignancy is a basal cell skin cancer, squamous skin cancer, or a cervical carcinoma in situ.
• Patient with Grade III/IV cardiac problems as defined by the New York Heart Association Criteria. (i.e., congestive heart failure)
• Patients with myocardial infarction within 6 months of study.
• Female patients who are pregnant or breast-feeding.
• Patient has a severe and/or uncontrolled medical disease (i.e., uncontrolled diabetes, chronic renal disease, or active uncontrolled infection).
• Patient has a known untreated or unstable brain metastasis.
• Patient has known chronic liver disease (i.e., chronic active hepatitis, and cirrhosis).
• Patient has a known diagnosis of human immunodeficiency virus (HIV) infection. HIV patients are at much greater risk of infection when receiving highly myelosuppressive agents (cisplatin, pemetrexed, and imatinib) and for safety reasons are not eligible for this trial.
• Patient who received prior chemotherapy for their malignant mesothelioma with the exception listed in inclusion criteria #7.
• Patient previously received radiotherapy to >/= 25 % of the bone marrow.
• Patient had a major surgery within 2 weeks prior to study entry.
• Patient with any significant history of non-compliance to medical regimens or with inability to grant reliable informed consent.
• Patients must agree not to use herbal remedies or other over-the-counter biologics (i.e. shark cartilage).
• Prior exposure to imatinib mesylate.
• Patients taking therapeutic levels of warfarin. However, patients receiving 1 mg daily for catheter related anticoagulation are eligible for the study.