A simplified method is proposed to treat the dynamic response of rigid embedded structures in either a full or a half-space subjected to plane P-waves. The soil-structure interface is discretized into a finite number of strips, resulting in an analysis which involves only plane surfaces and plane waves. Interaction forces on any strip are determined easily, and the contributions from all the strips are superposed to obtain the resultant forces and torque on the structure. Equations of motion then yield the steady state response of the structure. The Green function for the structure is obtained by Fourier synthesis, and the transient response to any other excitation is then obtained by using the Green function and the Duhamel integral. The entire analysis can be conveniently programmed.