Taking into account the interaction between a structure and the soil bed during an earthquake is a vital task of the seismic resistance theory. Despite a large amount of research, there is no satisfactory solution of this problem at the time being. The "platform model" applied in engineering practice can be used only for homogeneous soil beds. However, the surface stratum of soil, as a rule, has a multilayer structure, in which each individual layer has its own physical and mechanical characteristics determining the resonant properties of the entire system. The standard methods of analysis do not take into consideration the heterogeneity and layered nature of a soil bed using the averaged stiffness characteristics, which does not allow evaluating the specific features of resonance processes during the joint oscillation of a building and its soil bed. In addition, the dynamic characteristics of soils have a rather high statistical variability even within the same layer, and this can significantly affect the distribution pattern of the resonant frequencies of the system. The present article is aimed at investigating the dynamic response of the “building – multilayer soil bed” system based on the analytical model of a horizontal layered medium. The following tasks were solved: – an analysis of a layered system under the action of a complex sinusoidal signal was carried out with regard to damping; – the amplitude-frequency characteristics were constructed both for individual layers and for the system as a whole; – the influence of the statistical variability of the velocity of transverse seismic waves propagation on the resonant frequencies of the layered system under consideration was assessed. The analytical methods for the solution of the wave problem of seismology were used.