The paper investigates the effect of soil-structure interaction on the dynamic response of structures. A non-parametric probabilistic formulation for the modelling of an uncertain soil impedance is used to account for the usual lack of information on soil properties. Such a probabilistic model introduces the physical coupling stemming from the soil heterogeneity around the foundation. Considering this effect, even a symmetrical building displays a torsional motion when submitted to earthquake loading. The study focuses on a multi-story building modeled by using equivalent Timoshenko beam models which have different mass distributions. The probability density functions of the maximal internal forces and moments in a given building are estimated by Monte Carlo simulations. Some results on the stochastic modal analysis of the structure are also given.