Numerical flow simulations are useful for understanding pressure wave propagation in circulatory systems. Our one-dimensional numerical model, which encompasses the effect of unsteady viscosity and the generalized viscoelasticity of tubes, has previously indicated that the tube's viscoelasticity plays an important role in the wave propagation. In the present study, in order to investigate the relationship between changes in the viscoelastic properties of the tube and periodic blood pressure wave propagation. A one-dimensional numerical model of wave propagation in a silicone tube was validated quantitatively and the approximation error of the model was estimated. By analyzing the calculated results using these models with the parameter change of a viscoelastic property of the tube, we can make the following conclusions. The pulse wave velocity and the pulse pressure increase from increasing of the viscoelasticity of the tube. The tube viscoelasticity also plays an important role in the periodic blood pressure wave propagation, and the arterial stiffness index affect by the blood vessel viscoelasticity.