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In this paper, the buckling behaviour of rectangular and skew plates with elastically restrained edges subjected to non-uniform mechanical edge loading is investigated. An analysis method is developed for calculating the critical buckling load of plates using the Ritz method under non-uniform mechanical edge loading, in which the shape function is expressed as Legendre polynomials. The in-plane stress distribution under non-uniform mechanical edge loading is defined by the pre-buckling analysis. Contributions of elastic boundary conditions are taken into accounted by giving different edge spring stiffnesses. The proposed method for buckling analysis of plates is validated by the comparison of exiting results in literature. Finally, the effects of the edge restrained stiffness, non-uniform edge loading, skew angle, aspect ratio and combined compression-shear load are discussed by parametric analysis.