In order to accurately determine the dynamic response of cross-ply laminated thick plates subjected to moving load, a solution procedure based on the three-dimensional (3D) elasticity theory is presented. Plates with simply supported edges and subjected to point moving load are considered. The layerwise theory is used to discretize the equations of motion and the related boundary conditions through the thickness of the plates. Then, the modal analysis in conjunction with the differential quadrature method is employed for the in-plane and the temporal discretization of the resulting system of differential equations, respectively. The convergence behavior of the method is demonstrated and to show its accuracy, the results are compared with those of the exact solutions obtained for the isotropic plates under moving load and other available solution. Comparisons between the results of the 3D elasticity solutions and those of the first order shear deformation theory (FSDT) and the higher order shear deformation theory (HSDT) for the cross-ply laminated plates are also made to show the effectiveness of these theories. The effects of the thickness-to-length ratio, load velocity, load eccentricity and lamina layout on the response of the plate are studied. Due to high accuracy of the method, the results can be used as benchmarks for future research.