There are a large number of works on a comprehensive assessment of the seismic resistance of buildings and structures. However, these studies, as a rule, do not take into account the random nature of the seismic impact, which is a pronounced non-stationary random process. An adequate assessment of the seismic resistance of buildings and structures is possible only on the basis of methods that allow taking into account the large variability of seismic impact parameters. The article presents a probabilistic method for calculating multi-storey reinforced concrete buildings designed in seismic regions, taking into account the interaction of a building with a non-linearly deformable foundation. The developed technique makes it possible to provide the required level of seismic resistance for the designed buildings based on the non-collapse criterion. As an ex-ample, the calculation of a multi-storey reinforced concrete building is considered. External seismic action is represented as a non-stationary random process. The external seismic action is considered as a non-stationary random process, which is obtained by multiplying the stationary random process by a deterministic envelope function. The parameters necessary for constructing the envelope and the stationary random process were obtained from the results of processing the available database of intense earthquakes. The stationary random process was generated by the shaping filter method. The impact parameters are based on the results of processing the available database of intense earthquakes. When modeling reinforced concrete structures, a concrete model is used with the function of damage accumulation under cyclic loads, as well as taking into ac-count the degradation of the strength and stiffness of the material during an intense earthquake. Accounting for the interaction of the building with the soil base is implemented using the SSI interface (Soil Structure Interaction). To prevent the influence of waves reflected from the boundaries of a limited ground massif, a PML layer (Perfectly Matched Layer) is used. The calculation was carried out using explicit methods for integrating the equations of motion on a computing cluster using parallel computing technology. The presented technique makes it possible to investigate the nature of the destruction of reinforced concrete structures during intense earthquakes and to identify zones with a deficiency in bearing capacity. The proposed probabilistic approach to modeling seismic impact as an implementation of a non-stationary random process with given parameters, together with taking into account the nonlinear deformation of the reinforced concrete structures of the building and foundation, allows you to control the level of reliability and design buildings with a given seismic resistance.