In this study, a pulsatile flow of a viscous incompressible fluid through an elastic straight tube witha mild stenosis whose amplitude oscillates in its radial direction was investigated. The distributionof pressure and pressure gradient was obviously different from those of flow through a straight tubewith an static stenosis. And it is closdy connected with Wormersley parameter, character of thewall of the tube, and the frequency of the stenosis amplitude oscillation. This study is important forfurther analysis of certain pathology or curative method.