Abstract: An input method of obliquely incident earthquake for a layered site with step-shaped topography is developed based on the viscous boundary and the horizontal layered site response analysis method under obliquely incident earthquake. The input wave fields at lateral boundaries are the free field responses of a horizontal layered site. Each lateral boundary uses the site with identical parameters as a lateral boundary, and therefore two lateral boundaries use the different site models. The input wave field at the bottom boundary is an incident wave field. Because above treatments, the input method is approximate. The factors affecting the accuracy of the method have been discussed, such as boundary location, inputted earthquake, the angle of incidence, slope inclination, and layered media. The results indicate that the peak error of displacement is less than 5% for all kinds of cases studied in this paper under the SV wave. The accuracy of the proposed input method of obliquely incidence earthquake satisfies the engineering requirements, and the method can be used for seismic response analysis of a step-shaped topography site.