This thesis deals with the effects of soil-structure interaction, both kinematic and inertial, on the responses of seismically excited rectangular foundations and simple structures supported on such foundations. The ground motion considered is defined stochastically by a local power spectral density function and a spatial incoherence function. The structures examined are considered to have one lateral and one torsional degree of freedom in their fixed-base condition. The response quantities investigated include the ensemble means of the peak values of the lateral and torsional components of the foundation input motion and of the associated structural deformations. These responses are evaluated and compared with those obtained for no soil-structure interaction and for kinematic interaction only. The information and concepts presented elucidate the nature and relative importance of the two effects and make it possible to assess readily the influences of the more important parameters involved.