Abstract: Thin rectangular plates under non-linearly distributed edge loads are very common in engineering. Accurate stress distribution is required for buckling analysis of thin plates. Because of the complexity, no exact solution has been given thus far. Ritz method is used to find the distribution of in-plane stresses of thin rectangular plates under non-linearly distributed edge loads based on the theory of elasticity. Chebyshev polynomials are adopted as the stress functions which satisfy the stress boundary conditions. The stress distributions of rectangular plates with different aspect ratios under uniaxial or biaxial parabolic edge compressions are analyzed with the help of mathematic computational software Mathematica. It is seen that results satisfy exactly the stress boundary conditions and agree very well with numerical results given by finite element method and differential quadrature method, thus, verify the validity and accuracy of the proposed method. The results lay a foundation for the buckling analysis of rectangular plates under non-linearly distributed edge loads.