The presence of hemodynamic factors could localize vascular disease in regions of complex flow, occurred due to branching, bifurcations, and curvature of the arteries in the coronary, carotid, abdominal, and femoral arteries. These factors could produce severely atherosclerotic regions in the mentioned arteries. For instance, in the carotid artery, atherosclerotic lesions localize along the outer wall of the carotid sinus region where the wall shear stress is low [Zarins et al., 1983]. The bypass graft implantation surgery is a common procedure for patients with significant stenosis in their arteries. However the patency of such a surgery strongly depends on the choice of blood vessel(s) used for the revascularization [Lytle et al., 1985]. Various experimental and numerical investigations have been performed trying to reveal the contribution of different hemodynamic factors in the long term success of arterial bypass surgery such as recirculation, vortex motions, and shear stress distributions on the artery wall. For example, an intimal hyperplasia at arterial bypass graft anastomoses has been stated as the major factor responsible for the graft failure [Cole et al., 2002]. However, the exact nature of the two way interaction between the dominant pulsing flow and the deformable structure of the arteries has not been fully investigated numerically.