The numerical methods have been widely used to solve the structure-foundation interaction problems in which the semi-infinite medium simulation and the external excitation input method are of most concern． The com- monly used external excitation input methods include the wave method，the artificial boundary substructure method and the domain reduction method ( DＲM) ，etc． Firstly，the applicability of different wave input methods for single- phase media e are compared by virtue of FLAC3D and Matlab，and the results show that the free field response ob- tained by the DＲM method match well with the one-dimensional analytical solution． Further，the artificial boundary substructure method and DＲM method are applied to porous medium，respectively，and the formula to transfer ex- ternal excitation into equivalent force and equivalent discharge are proposed． Finally，the feasibility of two methods are compared and verified with the elastic semi-infinite saturated foundation response under the effect of vertical seismic wave． The results indicate that the free field response value obtained by the DＲM method is consistent with the one-dimensional analytical solution，however，the response value obtained by the artificial boundary substruc- ture method is much smaller．