Buckling and free vibration analysis of simply supported symmetric and antisymmetric cross-ply thick composite plates on elastic foundation are examined by a new hyperbolic displacement model in this paper. In this new model, inplane displacements vary as a hyperbolic function across the plate thickness, so account for parabolic distributions of transverse shear stresses and satisfy zero shear stress conditions at the top and bottom surfaces of the plate. In the analysis, the foundation is modeled as two parameter Pasternak type foundation, and Winkler type if the second foundation parameter is zero. The equation of motion for thick laminated rectangular plates resting on elastic foundation and subjected to inplane loads is obtained through Hamilton's principle. The closed form solutions are obtained by using Navier technique, and then buckling loads and fundamental frequencies are found by solving the results of eigenvalue problems. The numerical results obtained through the present analysis for free vibration and buckling of cross-ply laminated plates on elastic foundation are presented, and compared with the ones available in the literature.