In this study, the analytical expressions of pressure and wall shear stress in local vessel expansion region were deduced through solving the linear blood now equations. with the assumption of the development process mode of the local vessel expansion with time, the progresses of the pressure and wall shear stress in local vessel region were discussed. Results show that in the local vessel expansion section, the pressure is slightly larger than that in the uniform vascular section, and that the shear stress decreases significantly, which will have some effects on vessel tissues.