The characteristics of blood flow and the interaction between the blood vessel and blood flow play important roles in plaque cap rupture and the growth of atherosclerosis which may lead directly to a heart attack or a stroke. In this study, carotid arteries with different stenoses have been numerically simulated to investigate the wall shear stress(WSS) and the elastic motion of the vessel. Blood flow has been treated as physiological, laminar and incompressible flow. To model the shear thining behavior of the blood, the Carreau-Yasuda model has been employed but the viscoelasticity of blood has not been considered. The results show that the WSS of $severe(75\%)$ stenosis is much higher than those of $25\%;and;50\%$ stenosis in the region of stenosis. With the increase in the stenosis thickness, the expansion ratio of the center of the stenosis decreases while the expansion ratio of the upstream region of the stenosis increases.