In the twenty-first century, the seismic design of buildings seems to have become a fully recognized topic. There are guidelines and standards which should be taken into account by designers in seismic areas. Designers using modern international guidelines have ascertained that the behavior of structures is not as expected. New challenges in the construction industry result in the construction of structures with new, unusual shapes. These are structures that do not meet the assumptions of safe construction in seismic areas. Contemporary buildings are also characterized by their irregular distribution of structural elements. Such solutions are not beneficial from the point of view of seismic engineering and can lead to reduced dynamic resistance and damage in such structures. In this paper, a five-storey, irregular-shaped reinforced concrete (RC) building model was subjected to different earthquakes with varying magnitudes, PGA (peak ground acceleration) and PGV (peak ground velocity) values, and durations of the intense shock phase. Once the model was verified using previous in situ measurements, the building model was subjected to five earthquakes. A numerical nonlinear analysis of the building was performed using a verified FEA (finite element analysis) model in the time domain through non-linear time history analysis with the Broyden–Fletcher–Goldfarb–Shanno (BFGS) method. The building’s dynamic properties were measured using various methods of excitation. The model was influenced, among others, by two far-field representative events caused by the last earthquake in Turkey, which resulted in strong ground motion. The analysis results identified the locations of structural damage and allowed for the assessment of the structure’s dynamic resistance. The results of the calculations prove that the duration of the intensive phase of extortion is one of the reasons for building damage in earthquake-prone areas. Building damage occurs with earthquakes that are characterized by an intensive phase of excitation with a long duration and high values of velocity in the earthquake components. The article highlights the inadequate dynamic resistance of the building, leading to excessive displacements and unfavorable structural solutions. Damage to buildings at this earthquake intensity caused damage to the load-bearing structure, which was not designed for such intensities. This paper is a research report with a specific case study of medium-rise irregular RC buildings.