The protection and safeguard of historic masonry constructions in seismically active areas represents one of the most complex and relevant challenges in the field of Civil Engineering. Our architectural and archaeological heritage has specific vulnerabilities that make it highly susceptible to damage caused by earthquakes. Therefore, it is necessary to develop appropriate theoretical approaches to the study of the dynamic behavior of these structures that allow to prevent the most common collapse modes and to design wise interventions for the conservation and safeguard of the historic-monumental building. The approach mainly used for the study of the dynamics of archaeological structures and curved masonry structures is based on the studies of Housner: the dynamics of the “rocking” of structures made of rigid blocks. The Authors have formulated a new method for the characterization of dynamics of masonry structures, one of the objectives of which is presented in this work: the analysis of the influence that the damage caused to the edges of the blocks during rocking may have on the overall dynamic behaviour of the structure. For this purpose, a new analytical model was developed by introducing a “connected” geometry for damaged edges of rigid blocks described by new geometric parameters. This approach allowed to analyze the variations of the block stability and its energy dissipation during the oscillatory motion. By numerical models developed in Matlab, the proposed model was compared with the traditional model, considering different seismic load scenarios. Furthermore, experimental tests with dynamic shaker were conducted on small-scale concrete blocks, both with straight edges and with rounded edges. These blocks were tested on surfaces of different materials, a choice motivated by the need to investigate the dependence of the dynamic response on the mechanical properties of the materials, in a way different from what has already been studied in the literature.