Abstract: 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).