This paper applied polynomial displacement functions for free-vibration study of isotropic thick rectangular plates. The theory uses a third-order polynomial to describe how the transverse shear stress varies across the thickness of the plate and has no need for a shear correction factor. Polynomial expressions were used as the displacement functions (u, v and w) and also as shear deformation function f(z) in obtaining the general governing equations for the plate. For numerical illustrations, a thick rectangular plate whose four edges have simple supports (SSSS) was studied. The requirements for the edge conditions of the simply supported plate were satisfied and used in solving the general governing equation. This resulted to a linear equation used to generate for the plate, the non-dimensional fundamental natural frequency parameters for any value of span-thickness relation (a/t) and in-plane relation (b/a). To validate this study, results obtained herein were compared with related previous works in literature.