The seismic response of a flexible three-dimensional structure supported on a rigid circular foundation resting on an elastic half-space when subjected to a spatially random free-field ground motion is studied. Results illustrating the effects of spatial randomness are presented for a 10-story building and for a containment building in a nuclear power plant. The effects of spatial randomness include a reduction of the high-frequency components of the translational response along the axis of the structure and the generation of significant rocking and torsional response components which also affect the motion on the perimeter of the structure.