Abstract: This paper presents a discrete process for boundary integral equation using the semi-analytical finite element. The three-Dimensional elastodyanmic problems have been simolified into one-dimensional numerical calculations by semi-analytical process twice of fun lamental solutions and trial functions. The moving boundary element method is used to describe the wave propagation in half-space. Some exam es such as wave propagation and wave diffraction were studied to show the higher accuracy, less computation work and great benifit of the numerical soultion.