Dynamic response of moderately thick antisymmetric cross-ply laminated rectangular plates on elastic foundation is investigated. The governing equations are based on the higher order shear deformation theory (HSDT). Two-parameter elastic foundation (Pasternak type) is considered. Modal analysis in conjunction with the incremental differential quadrature method (IDQM), as an efficient and stable numerical tool for temporal domain discretization, are employed to solve the governing differential equations. Much lower computational time of the DQM with respect to Newmark’s method is exhibited. The convergence of the method is demonstrated and its accuracy is shown by comparing the results with those of exact solution for thin plate obtained using the classical plate theory (CPT). Also, comparison between the results of different theories, i.e. the classical thin plate theory (CPT), the first order shear deformation theory (FSDT) and the higher order shear deformation theory (HSDT), is made. The effects of different parameters on dynamic response of the antisymmetric cross-ply plates are studied. The results can be used as benchmark solution for future works.