Plates supported on elastic foundations are found in many civil engineering applications. The analysis requires a critical understanding between the plate element and the foundation. The objective of this study is to come up with a better, simple, and easy analytical method that could be used for the analysis of all-round simply supported plate on Winkler's elastic foundation. The scope of the work includes static analysis of an isotropic simply supported rectangular plate resting on an elastic foundation carrying a uniformly distributed load. In this paper, characteristic orthogonal polynomials (COPs) shape functions for all-round simply supported rectangular plate on an elastic foundation were formulated by using Galerkin variational Energy method. The COPs shape functions formulation had been carried out by direct integration of the governing differential equation of the plate with those of elastic foundation using the Winkler model for the elastic foundation. The results obtained are very close to the results obtained by earlier research works that used different methods.