This dissertation is composed of two parts. In the first part, a comprehensive study is made of the harmonic response of a rigid mass or a mass-sprint system supported on a pile driven in a homogeneous elastic medium. The objectives are to assess the effects of the various factors that affect the response of the system. The second part deals with the harmonic response of rigid and elastically supported simple systems on pile groups. The main aim is to incorporate pile-to-pile interaction and investigate its effect on response of such systems. The system is shown to respond essentially as a viscously damped single-degree-freedom oscillator. Plots are presented for the amplification factor and the resonant frequency of the system. With the information presented herein significant aspects of the dynamic response of vertically and laterally excited simple structure-pile systems may be evaluated readily.