In this study, the analysis of thick plates resting on elastic foundation is investigated by using four-noded (PBQ4) and eight-noded (PBQ8) quadrilateral finite elements based on Mindlin plate theory and by taking into account transverse shear deformations. In order to avoid shear locking problem in case of small thicknesses, selective reduced integration technique is used in addition 1:0 full integration technique for the evaluation of the stiffness matrices of both elements. Various loading and boundary conditions are considered and a reference example is solved for comparison. It is concluded that the results obtained by using PBQ4 and PBQ8 elements are both satisfactory for thicker plates. However selective reduced integration technique is more reliable for thinner plates.