The paper considers a bi-material with a crack propagating rapidly, penetrating or deflecting at the interface under dynamic loading. The hybrid time-domain boundary element method, together with the multi-region technique, is applied to simulate the dynamic process of propagation and penetration or deflection of the crack. Moving of the crack tip in the matrix, penetration and deflection of the crack at the interface, and propagation of the crack along the interface are controlled by criteria developed from the quasi-static ones. A bi-material rectangular plate with an edged crack under impact loading is computed and compared with the photoelastic experiments. Good agreement between numerical and experimental results implies that the present boundary element numerical method can provide an excellent simulation for the dynamic crack propagation in a bi-material involving interfaces.