Discrete-time　rational　approximation　(DRA)　of　foundation　frequency　response　is　the　first　step　for　constructing　various　time-domain　recursive　evaluations　(TDREs)　in　foundation　vibration　analysis.　The　stability　and　accuracy　of　DRA　determine　those　of　its　TDREs.　In　this　paper,　the　stability　and　identification　of　DRA　are　studied.　The　DRA　can　be　obtained　from　a　continuous-time　rational　approximation　(CRA)　of　foundation　frequency　response.　If　the　discrete-time　frequency　is　set　to　equal　the　continuous-time　one,　the　high-frequency　loss　and　the　aliasing　may　occur　due　to　the　periodic　nature　of　DRA.　To　prevent　this　occuring,　the　bilinear　transform　is　used　in　this　paper,　so　that　the　stability　and　accuracy　of　the　resulting　DRA　are　identical　with　those　of　CRA.　The　resulting　DRA　is　realized　as　the　direct-form　and　parallel-form　TDREs　by　partial-fraction　expansion.　The　effectiveness　of　bilinear　transform　is　verified　by　analyzing　several　typical　foundation　vibration　problems　using　the　resulting　TDREs　and　comparing　with　the　results　of　lumped-parameter　models　(LPMs).