The dynamic behavior of structures of two stacked rigid blocks subjected to ground excitation is examined. Assuming no sliding, the rocking response of the system standing free on a rigid foundation is investigated. The analytical formulation of this nonlinear problem is quite challenging. Its complexity is associated with the continuous transition from one regime of motion to another, each one being governed by a different set of highly nonlinear equations. The behavior is described in terms of the four possible modes of response and impact between the two blocks, or the first block and the ground. The exact (nonlinear) equations governing the rocking response of the system to horizontal and vertical ground acceleration are derived for each mode. Furthermore, a comprehensive model governing impact is derived using classical impact theory. Finally, a computer program is developed to approximate the response of the system under arbitrary base excitation.