Abstract: A time-domain method for computing foundation impedance force is proposed in this paper. The high-order ordinary differential equations in time are first obtained from a stable and accurate continuous-time rational approximation (CRA) of foundation dynamic stiffness by introducing an auxiliary variable and performing inverse Fourier transform. The equivalent first-order system of ordinary differential equations in time as a state-space description is then obtained by defining above auxiliary variable in different instants as some different new auxiliary variables, whose stability and accuracy are identical with those of the CRA. The fourth-order Runge-Kutta formula is finally applied to solve the resulting first-order system. The effectiveness of the proposed method is indicated by analyzing several foundation vibration problems.