In the present article, the buckling analysis of thin functionally graded rectangular plates resting on elastic foundation is presented. According to the classical plate theory, (Kirchhoff plate theory) and using the principle of minimum total potential energy, the equilibrium equations are obtained for a functionally graded rectangular plate. It is assumed that the plate is rested on elastic foundation, Winkler and Pasternak elastic foundations, and is subjected to in-plane loads. Since the plate is made of functionally graded materials (FGMs), there is a coupling between the equations. In order to remove the existing coupling, a new analytical method is introduced where the coupled equations are converted to decoupled equations. Therefore, it is possible to solve the stability equations analytically for special cases of boundary conditions. It is assumed that the plate is simply supported along two opposite edges in x direction and has arbitrary boundary conditions along the other edges (Levy boundary conditions). Finally, the critical buckling loads for a functionally graded plate with different boundary conditions, some aspect ratios and thickness to side ratios, various power of FGM and foundation parameter are presented in tables and figures. It is concluded that increasing the power of FGM decreases the critical buckling load and the load carrying capacity of plate increases where the plate is rested on Pasternak in comparison with the Winkler type.

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