This open label pilot study will assess the (1) activity of methimazole (MMI), a down-regulator of MHC Class I transcription used in treatment of autoimmune thyroiditis (AIT), on the tissue expression of HLA class I and its (2) efficacy as measured by serum muscle enzyme levels and manual muscle testing in up to twenty patients with dermatomyositis (DM) or polymyositis (PM). Participants will have persistent weakness, laboratory evidence of inflammation and be on a stable regimen of medication to control their myopathy. MMI will be administered orally at 30 mg twice a day for six months. Patients will be evaluated for alteration of HLA Class I expression in muscle and peripheral blood lymphocytes (PBL) and drug-related toxicities during the study and for three months after the discontinuation of treatment.