Abstract: Based on Reissner-Mindlin first order shear deformation plate theory, the dynamic response of an initially stressed, moderately thick plate with four free edges resting on a tensionless elastic half-space foundation is presented. Initial stresses are induced by in-plane mechanical loads or temperature changes. The foundation is regarded as a three dimensional elastic half-space entity while its weakening deformation is considered. A set of pb-2 eigenfunctions, which effectively satisfies the free edge condition, is adopted, and Rayleigh-Ritz method is employed to determine the deflections and bending moments of the plate. Finally, the effects of initial membrane stress and thermal stress are studied.