This is a Phase IIa, single center, prospective open label clinical trial of Gleevec in patients with systemic sclerosis. All patients will be treated with active drug for 12 months. The primary objective of this study will be to determine the safety and tolerability of Gleevec in patients with systemic sclerosis, but important secondary outcomes of relevance will be improvement in disease status as defined by skin scores and indices of pulmonary function.