In order to apply the viscoelastic artificial boundary condition in the computation of a layered foundation model, the formulas for calculating the amplitude ratio of different types of seismic waves are derived in this paper based on the wave theory. The traveling wave effect is considered by the delay method and the free field of the layered foundation is solved, based on which the equivalent load considering the reflection and transmission of seismic waves is obtained. Finally, a viscoelastic artificial boundary model considering layered foundation is established. The vertical incidence of an SV wave is taken as an example to verify the formula and the proposed numerical model is then used in the dynamic calculation of a gravity dam. The results show that the model established in this paper satisfies the accuracy requirement of engineering seismic analysis and it can solve the problem of structural dynamic analysis considering soil-structure interaction when seismic waves spread vertically on the layered foundation.