An inward-propagating shock wave is shown to accompany the deceleration of an ejected supernova shell by the ambient medium. The gas behind this shock can be a strong source of soft thermal X-rays. We demonstrate that equipartition between the electrons and ions behind the blast wave moving into the circumstellar medium results in high electron temperatures and the production of hard X-rays. This model is applied to the young supernova remnants that are known to be X-ray sources and is shown to account for most of the observed features of the X-ray spectrum ofCasA. Subject headings: shock waves - supernova remnants - X-ray sources