Abstract: The localization of time convolution relation of generalized force and displacement has been the key to the construction of an pricise and infinite-domain FEM model used for the time-domain soil-structure-interaction analysis. The physical model method is used in this paper to localize time convolution as it is compatible to FEM. A novel model of high-order spring-dashpot-mass (HSDMM) is constructed using the time- and frequency-domain equations as well as the corresponding normal equations. The transformation relation for the parameters used in these two types of equations is also otained. The sufficient and necessary dynamic stability conditions for the proposed model are proposed, and a parameter identification method (PIM) considering stability condition is developed based on the penalty function and the genetic-simplex algorithm. The systemic and concise HSDMM with the proposed PIM can be readily incorporated into a dynamic commercial software and the established dynamically stable soil-structure interaction problem can be solved even using an explicit time stepping integration. Finally, the performance of HSDMM with the proposed PIM is evaluated by analyzing a semi-infinite rod on elastic foundation with it and comparing the results to the results obtained with several existing models.