The seismic safety of concrete dams is one of the important problems in the engineering due to the vast socio-economic disasters which may be caused by collapse of these infrastructures. The accuracy of the risk evaluation associated with these existing dams as well as the efficient design of future dams is highly dependent on a proper understanding of their behaviour due to earthquakes. This paper develops an anisotropic damage model for arch dam under strong earthquakes. The modified Drucker-Prager criterion is adopted as the failure criteria of the dynamic damage evolution of concrete. Some process fields and other necessary information for the safety evaluation are obtained. The numerical results show that the seismic behaviour of concrete dams can be satisfactorily predicted.