Abstract: The state-of-the-practice soil-structure interaction (SSI) of nuclear facilities are analyzed using the frequency-domain approaches, represented by the SASSI program. SASSI incorporates the strain-dependent characteristics of soils only indirectly, via the equivalent-linear method, and cannot account for non-horizontal layered soil case. SSI analysis in the time domain may capture non-linearity of materials in the soils and geometric nonlinearity in the foundation (gapping and sliding), but now it is not efficient in practice. In this study, a computationally efficient explicit-implicit FEM in parallel manner to analyze the response of three-dimensional soil-structure system subjected to three-direction seismic waves is proposed. The unbounded soil is modelled by the lumped-mass explicit finite element method and viscoelastic artificial boundary, the structure is analyzed by the implicit finite element method, and the response of the rigid foundation is calculated by the explicit time integration scheme. Different time steps can be chosen for the explicit and implicit integration scheme, which can greatly improve the efficiency. The synchronous parallel algorithms using MPI are used. The codes for this method are programmed. An example for seismic response analysis of a nuclear plant on non-horizontal layered site is given to validate the feasibilty and efficiency of the proposed method.