The studies performed in the doctoral dissertation focused on estimation of the seismic response of some of the most typical reinforced concrete (RC) building structures, i.e. frame structures, cantilever wall structures and dual structures composed of frames and cantilever walls. The seismic response of structures was calculated by taking into account record-to-record variability (randomness) and modelling uncertainty. The spectral acceleration at the period of the equivalent SDOF model Sa (T*) was used as the intensity measure. Default dispersion measures were proposed for the considered structures, based on extensive numerical studies of a portfolio of archetypal structural systems, which have contributed to the development of the practice-oriented risk assessment methodology based on the N2 method and predetermined dispersion measures. The identification of the structural parameters that influence the values of dispersion measures was also made, and their values were given. In addition, a simplified procedure for seismic response assessment with consideration of uncertainty was proposed. The development of the proposed procedure relied on the determination of the so-called probabilistic single degree of freedom model (probabilistic SDOF model), which allows approximate simulation of modelling uncertainty. The major advantage of the proposed procedure is that both seismic response assessment and simulation of modelling uncertainty are performed at the level of the probabilistic SDOF model. Such an approach allows significant reduction of computational time in comparison to some existing procedures. The results of the proposed procedure were validated by the employment of more accurate procedures. It was shown that the proposed procedure allows a considerable reduction of computational efforts, but still provides comparable accuracy as some existing procedures.