The whole atherogenetic process should be considered as a net result of biological, chemical and mechanical interactions between the blood flow and the arterial wall. As common in all three types of interactions, they have several different time scales. Even in the context of wall mechanical responses, we should distinguish very short term, in other words, pure mechanical responses from intermediate and long term responses involving chemical and biological processes, which are results of an accumulation of the former. In our previous reports[1–2], the fluid motion and the wall motion in models of the arterial stenosis and the abdominal aneurysm with thick deformable walls was computed. In the present study, we are interested in some intermediate process in which the arterial wall changes its mechanical properties, and computed the fluid-wall interactions with different stiffness of the lesion.