Historical buildings in seismically active regions are severely damaged by earthquakes, since they certainly were not designed by the original builders to withstand seismic effects. In particular the reports after major ground motions indicate that earthquake-induced pounding between buildings may lead to substantial damage or even collapse of colliding structures. The research on structural pounding during earthquakes has been recently much advanced, although most of the studies are conducted on simplified single degree of freedom systems. In this paper a detailed pounding-involved response analysis of three adjacent structures is performed, concerning the main bodies of the "Quinto Orazio Flacco" school. The construction includes a main masonry building, with an M-shaped plan, and a reinforced concrete building, separated from the masonry one and realized along its free perimeter. By the analysis of the capacity curves obtained by suitable pushover procedures performed separately for each building, it emerges that masonry and reinforced concrete buildings are vulnerable to earthquake-induced structural pounding in the longitudinal direction. In particular, due to the geometric configuration of the school, a special case of impact between the reinforced concrete structure and two parts of the masonry building occurs. In order to evaluate the pounding-involved response of three adjacent structures, in this paper a numerical procedure is proposed, programmed using MATLAB software. Both a non-linear viscoelastic model to simulate impact and an elastic-perfectly plastic approximation of the storey shear force-drift relation are assumed, differently from many commercial softwares which admit just one non-linearity.