Abstract: Compared to the traditional finite element method (FEM), one significant advantage for numerical manifold method (NMM) is not necessary to force the mesh to match the cracks, facilitating the simulation of failure in rock mass. Based on NMM containing enriched functions of crack tip, the Newmark implicit algorithm was used for time integration. Besides, emphasis was placed on the solution method of dynamic stress intensity factor (DSIF) of crack under dynamic loading condition. Numerical examples with NMM for typical elastic dynamic crack problems are presented. The results show that the NMM can not only accurately evaluate DSIF under dynamic loading condition, but also have very good convergence property to the theoretical solution.