The accuracy of the risk evaluation associated with existing dams as well as the efficient design of future dams is highly dependent on a proper understanding of their behavior due to earthquakes. This paper presents a 3D anisotropic damage model for arch dam under strong earthquakes. The modified effective Mohr–Coulomb criterion is adopted as the failure criteria of the dynamic damage evolution of concrete. From the simulation of the dynamic damage process, some process fields of the dynamic displacement, the dynamic stress, dynamic damage distribution and other necessary information for the safety evaluation are obtained. These results show that the seismic behavior of concrete dams can be satisfactorily predicted. This will provide a reasonable theoretical support on the safety evaluation of the capability for concrete arch dams against earthquake loading.