Abstract: The discrete-time rational approximation function is one of the important methods for establishing dynamic analysis model for foundations. The stability and accuracy of the rational function determine those of dynamic time history analysis. At present, the researches on the discrete-time rational approximation function mainly focus on the establishment of time-domain analysis model, but they cannot guarantee the stability, accuracy and calculation efficiency of the identification function at the same time. Based on the theory of system stability, the rational approximation function is regarded as the combination of first-order and second-order systems, and the stability boundary of identification parameters is derived according to the stability condition of its roots. On this basis, a time-domain stable parameter identification method is proposed by using the genetic algorithm and the sequential quadratic programming algorithm. The stability and accuracy of parameter identification are verified through numerical simulation of different frequency response functions for foundations. Due to the boundary of parameter range, the calculation efficiency is also greatly improved.