Abstract: The analytical solution for a rectangular thin plate on foundation with four edges free was derived by the double finite cosine integral transform method.In the analytical process the elastic foundation was regarded as Winkler foundation model.Only the basic elasticity equations of the thin plate on elastic foundation were used and it was not needed to first select the deformation function arbitrarily.Therefore,the present solution was reasonable.In order to prove the correctness of formulations,the numerical results were also presented to compare with those of other references.