Numerical models of several typical masonry buildings are constructed. Building responses (expressed by level of effort, stresses and degradation level) to semi-seismic ground tremors for two limiting models of joints between floors and walls (the pivotal one and the fixing one) are compared. The plastic degradation BARCELONA Model proposed for concrete by Lubliner is applied to model the building materials (concrete and masonry). This model takes into account two different degradation mechanisms separately for compression and tension. To obtain a realistic evaluation of the hazard areas of masonry buildings, several numerical analyses of several models of construction are investigated. Typical buildings with different number of floors are analyzed. The numerical models are subjected to digitally recorded kinematical enforcements (with different spectral characteristics) which are the most dangerous for real buildings. The nonlinear plastic-damaged model of material permits to obtain maps of stresses without non-physical values (e.g. stress concentration) and maps of degradations, which are qualitatively similar to crack areas observed at damaged buildings.