Low computational efficiency and non-linearity behaviour make the simulation of the overall building structure problematic to attain with a single dynamic or static method. Thus, this paper uses a plastic deformation (PD) method based on concrete plasticity theory (CPT) for comparative analysis of multi-storey reinforcement cement concrete (RCC) and composite buildings under common and rare earthquake loads. For this purpose, a 15-storey tall building was selected for analysis using ABAQUS software. At first, a possible building model was created and then plastic deformation analysis was performed using the new PD method under both common and rare earthquakes. After that, a nonlinear time history analysis was conducted, and the results of plastic strain distribution, lateral displacement, peak acceleration, storey stiffness, shear force, storey drift, normalised shear, and top deflection of the RCC and composite buildings were studied deeply. The fundamental time period of the RCC model was found to be 5.2 s while the fundamental time period of the composite model was 6 s. Under common and rare earthquake leads, the peak acceleration of the RCC building was 19% and 22% higher than composite buildings, respectively. Under common and rare seismic loads, the top deflections of the composite building were 33% and 36% higher than those of RCC buildings, respectively. In the case of the RCC building, it was found in this study that higher peak acceleration (PA) of the ground motion led to higher storey top displacement, storey drift, shear force and top deflection under both ground motions. Numerical results suggested that the use of composite structure is more durable than RCC structure. It was also concluded that the PD method could also be effectively used for the analysis of RCC and composite buildings under dynamic loads.