Abstract: Due to the anisotropy widely exists in underground rocks, and with the increasing of exploration precision, isotropic hypothesis of underground media can't be gradually content with the status quo, so the numerical simulation of the anisotropic medium is more important. This paper derived the elastic wave equation of anisotropic medium, summarized the source type, tackled the problem of the artificial boundary by PML method, and verified the numerical dispersion and stability conditions by snapshots. The results show that: 1) PML based on staggered grid can solve the problem of the artificial boundary; 2) reduce the spatial sampling interval is much better than reduce time sampling interval to suppress numerical dispersion and blindly reduce time sampling interval can reduce the operational efficiency of the numerical simulation; 3) there is quasi p-wave and slow quasi s-wave in the elastic wave field of anisotropic medium; 4) quasi p-wave front energy is stronger than quasi s-wave energy, quasi p-wave and quasi s-wave front are changed as parameters of anisotropic medium.