Abstract: For the slope terrain site, the asymmetric and irregular boundary conditions at the left and right sides extend to the far field, which makes it difficult to solve the ground motion waves. In order to obtain the seismic dynamic response of the layered slope terrain sites, based on the wave field theory, a computational model proposed for the scaled boundary finite element method (SBFEM) whose scaling center is the splicing lines. Firstly, the wave field to be determined is decomposed into the known wave field with regular boundary conditions and the scattered wave field caused by the real irregular boundary of the slope-shaped site in the known wave field. Then, the solution of the scattered wave field is transformed from the wave scattered problem to the internal radiation one by applying the equivalent seismic loads on the irregular boundary of the slope terrain site. Finally, the SBFEM, which is suitable for the foundation with horizontal and inclined layes and asymmetric left and right sides, is derived for the internal radiation problem of the slope terrain site analytically along the radial direction. The accuracy of the model is demonstrated by comparing the surface dynamic responses of the depressed terrain site in the uniform and layered elastic half-space under the SH wave incident in the literature, and the validity of the model is verified by analyzing the wave response of the slope terrain site in the layered half-space. The proposed model provides an alternative technique for calculation of the input wave field of the complex soil-structure interaction analysis.