The dynamic coupling between a building and its foundation medium during an earthquake type of motion is investigated by utilizing the solutions for the steady state response of a dynamically loaded rigid plate on an elastic half-space. The analysis considers both the translational and rotational stiffness of the foundation medium. The general formulation provides a rational approach for investigating the elastic interaction phenomenon of a building when its foundation is subjected to a periodic loading function in the horizontal direction. Numerical results are presented for the interaction response of some idealized buildings having properties which are representative of modern high-rise frame structures. All of the buildings were assumed to be supported on several different foundations, and the influence of the building-foundation phenomenon on the natural frequencies and motion of the building is examined for each case.