This is a parallel study with MSS-9116095. The objective is to involve stochastic analysis of failure probabilities for seismically excited systems exhibiting soil-structure interaction phenomena. The models considered will take into account kinematic coupling between the free-field motion of the soil and the rigid motion of the foundation, inertial coupling between the motion of the soil-foundation and the motion of the attached structure, and non-linear behavior of the soil medium. Both circular and rectangular surface supported rigid foundations will be considered. The applicability of simplified stochastic methods previously used primarily for structural engineering problems will be investigated by comparing their results with those of Monte Carlo numerical simulation.