The influence of random soil dynamical parameters on seismic vibrations of extended structures is studied. The excitation is modeled by vector random process. Soil dynamic parameters are supposed random variables stochastically independent on random excitations. The problem is solved as linear. General equations are given. A simple specific case is being considered: system with two elastically connected masses, each of them is situated on soil. The numerical results obtained show that accounting for random soil parameters may alter the system response significantly.