As historic monuments become more vulnerable to seismic hazard with time, it becomes essential to be able to assess the seismic hazard in a quantifiable manner. For soft soil foundations, a computer program such as SHAKE may be utilized. For stiff rocks comprised of layers and joints a discontinuous approach must be utilized. This approach can be extended to masonry structures, so as to find by means of numerical analysis the peak ground acceleration and frequency at which the historic monument is most vulnerable and to predict the anticipated failure modes. The numerical, discrete element discontinuous deformation analysis (DDA) method is used here for this purpose. We begin by demonstrating DDA's ability to model wave propagation through layered media using a theoretical example and a real case study. We proceed with comparing between thermally and seismically induced irreversible block displacements in jointed rock slopes at the foundation of Masada world heritage site, and finally we present two case studies of masonry structures in Israel that are prone to seismically induced deterioration due to their proximity to the active Dead Sea rift.