Much research in recent years has focused on the seismic analysis of concrete and earthfill dams, and few works have addressed the case of masonry dams. The structural behaviour of masonry dams is controlled essentially by its discontinuous nature, which may induce significant non-linear response during an intense earthquake. In this paper a numerical tool based on the Discrete Element Method is presented, aimed at the static, dynamic and hydromechanical analysis of masonry gravity dams. The use of discontinuous models is mandatory for the study of failure mechanisms involving the masonry discontinuities, the dam-rock interface or the rock mass joints. The Discrete Element Method is able to assemble continuous and discontinuous meshes simultaneously in the same model, providing a versatile tool to consider various assumptions and levels of analysis, ranging from simplified to detailed structural representations. A comprehensive study of the seismic behaviour of Lagoa Comprida Dam, located in Portugal, is presented. Both continuous and discontinuous models were developed to assess the main failure mechanisms, including overstress, partial and global sliding and overturning.