In order to solve the problem of massive amount of computation brought by the numerical dynamic response simulation of soil-structure nonlinear interaction (SSI) system, the parallel computing method using SSI load balanced and dual-graph theory based domain decomposition (DD) algorithm is proposed. Combined with traditional greedy and recursive coordinate bisection algorithm, the parallel performance of these four algorithms is researched. The SSI is dealt with symmetric penalty method. The system equation is solved using finite element method (FEM) with explicit central difference scheme. The dynamic responses of typical engineering problems with SSI are simulated in parallel, and the scalability of these four algorithms is analyzed. The results indicate that the SSI load balanced algorithm which substantially balances the coupling loads of soil and structure shows the best parallel efficiency, followed by dual-graph theory based algorithm and recursive coordinate bisection algorithm, and the greedy method get the lowest parallel efficiency; the parallel efficiency decreases with the increasing cores, and the number of cores should be chosen properly according to the scale of the actual model to achieve the optimal parallel performance; the explicit FEM with penalty method is a proper approach for SSI dynamic analysis.