An application is presented of a modified Vlasov model to earthquake analysis of plates resting on an elastic foundation. The effects of the subsoil depth, the plate dimensions and their ratios on the dynamic response are investigated. The method of finite elements is used for spatial integration and the Newmark-beta method is used for time integration. A number of graphs are presented to show the effects of plate dimensions and the subsoil depth on the dynamic out-of-plane responses of plates on elastic foundations. Numerical examples associated with the applicability of the model to earthquake analysis of plates resting on elastic foundations are given. (C) 1998 Academic Press Limited.