Abstract: Blood flow in artery was treated as the flow under equilibrium state(the steady flow under mean pressure) combined with the periodically small pulsatile flow. Using vascular strain energy function advanced by Fung, the vascular stress-strain relationship under equilibrium state was analyzed and the circumferential and axial elastic moduli were deduced that are expressed while the arterial strains around the equilibrium state are relatively small, so that the equations of vessel wall motion under the pulsatile pressure could be established here. Through solving both the vessel equations and the linear Navier-Stokes equations, the analytic expressions of the blood flow velocities and the vascular displacements were obtained. The influence of the difference between vascular circumferential and axial elasticities on pulsatile blood flow and vascular motion was discussed in details.