This paper proposes an analytical method to calculate the probabilistic response of a rigid foundation on a soil medium subjected to vertical excitations. The uncertainty of the shear-wave velocity in soil is considered in this study. Simplified models are used to simulate the dynamic behavior of the unbounded soil. Numerical studies have been conducted to investigate the cumulative density function and the response spectrum for the foundation displacement. The numerical results show that the proposed method can generate the probabilistic response close to the Monte-Carlo simulation results. It is also found that the effectiveness of the simplified model significantly influence the computing accuracy of the probabilistic foundation responses in dynamic SSI analysis.