Abstract: In the analysis of soil-structure seismic response or of near-field seismic wave propagations, the visco-elastic artificial boundary elements are often applied to transfer the infinite-domain problem into a finite-domain problem. Since the material parameters and the size of the visco-elastic artificial boundary elements are different from those of the internal medium elements, there are differences in the numerical stability conditions between the artificial boundary domain and the internal domain when the explicit time domain step-by-step integration algorithm is used. At present, however, there are no appropriate analysis methods and research results to determine the explicit numerical stability conditions and the stable integration time steps. In this study, we propose a stability analysis method for explicit time-domain stepwise integration algorithm when using the two-dimensional visco-elastic artificial boundary elements. Firstly, several typical local subsystems of the artificial boundaries are established. The transfer matrix of each subsystem is analyzed, and the analytical solutions of the stability conditions for each subsystem are obtained. By comparing the stability conditions of the subsystems and the internal medium system, a uniform stability condition of explicit time domain stepwise integration algorithm is obtained when using the visco-elastic artificial boundary elements. When the internal medium areas also satisfy this stability condition, this condition becomes a sufficient condition for the stability calculation of the overall system and can be used to deciding the stable discrete time step in the numerical analysis.