The effect of the mechanical properties of a heterogeneous part on pulse wave has been investigated by using a one-dimensional lattice model associated with the material nonlinearity of the arterial vessel wall (an extended Sakanishi model). In the present study, from the viewpoint of mechanics, a part of blood vessel, which has the different mechanical properties of the arterial vessel wall, that is, a part of arteriosclerosis, prosthesis and so on, is regarded as the heterogeneous part by a generalization. The stability of the solitary wave is applied in order to obtain the reliable results by the numerical analysis of the pulse wave which propagates through the heterogeneous part in the blood vessel. As a result, the behaviors of the pulse wave and the mechanical factors which have the effects on the propagation of the pulse wave are shown. Moreover, a mechanical condition for the appropriate joining of the prosthesis is derived.