Studying the stress waves propagation in the elastoplastic half-plane domain is great value for predicting and evaluating environmental vibrations generated in dynamic engineering activities. To accurately simulate the stress waves propagation in an elastoplastic half-plane medium, the integral equations of time domain boundary element method were established based on the full space. Only the boundary and yield domain need to be meshed, and an adaptive semi-infinite boundary element was constructed to simulate the semi-infinite boundary, which can adjust its size in real-time with the propagation of stress waves. The outer node of the element was exactly located at the front of the stress wave to fully consider the influence of the semi-infinite domain on the propagation of stress waves. The proposed method was verified by the elastoplastic half-plane problem with a semi cylindrical groove subjected to explosive loads, and the results were compared with those of finite element method, elastic time domain boundary element method and ordinary elastoplastic time domain boundary element method. It is shown that the proposed method can effectively simulate the influence of stress wave propagation in a semi-infinite domain, and accurately simulate the propagation of stress waves in an elastoplastic half plane domain with a small number of mesh discretization.