abstract An analytical expression describing the three-dimensional vertical soil-structure interaction effects is developed using Laplace and Hankel transformation techniques. Utilizing these transformation techniques and normal mode theory of vibration, an N-mass structural model is coupled to an elastic half-space representing the earth. The resulting interaction equation is solved by numerical iteration techniques for a model of a nuclear power plant subjected to actual earthquake ground excitation. The effects of the soil-structure interaction are evaluated by comparing free-field acceleration spectrum response curves with similar curves determined from the foundation motion. These effects are found to be significant for structures typical of modern nuclear power plants subjected to seismic ground motions.