In this parametric study, the effects of soil-structure interaction on the earthquake response of structures is demonstrated by including various types of supporting media and seismic environments in the analysis of a very simple structure representing residential building. The effect of the type of control point selected is also addressed. The analyses are performed in frequency space by employing the substructure method and non-dimensional variables. The transformation from the frequency to time space is performed by FFT algorithm. The results are presented in the form of plots of maximum lateral (or torsional) acceleration against a reference period for various parameters appearing in the analyses.