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.