A simple approach using a Fast Fourier Transform (FFT) algorithm for obtaining the transient structural response to earthquakes is presented. Two different foundation models are used, a rigid circular plate and a rigid two-dimensional strip bonded to the elastic soil half space. A numerical procedure is used to obtain all pertinent transfer functions which are subsequently used in conjunction with FFT subroutines to obtain the response time histories. It is shown that over a range of scaled wave numbers which characterize the soil properties, significant base rocking can be expected only when either the slenderness parameter or the mass-ratio parameter is small. The specific advantages of the new approach are: (1) it is computational efficient; (2) it can take into account the frequency-dependent interaction forces; and (3) it is general, readily adaptable in practical applications, and can be used with any linear structure or interaction model.