The two-variable refined plate theory is used in this paper for the analysis of thick plates resting on elastic foundation. This theory contains only two unknown parameters and predicts parabolic variation of transverse shear stresses. It satisfies the zero traction on the plate surfaces without using shear correction factor. Using the principle of minimum potential energy, the governing equations for simply supported rectangular plates resting on Winkler elastic foundation are obtained. The Navier method is adopted for solution of obtained coupled governing equations, and several benchmark problems under various loading conditions are solved by present theory. The comparison of obtained results with other common theories shows the excellent efficiency of this theory in modeling thick plates resting on elastic foundation. Also, the effect of foundation modulus, plate thickness and type of loading are studied and the results show that the deflections are decreased by increasing the foundation modulus and plate thickness.