Abstract: A new semi-inverse method based on the Airy stress function is proposed for elastic plane problems, especially for wedges in polar coordinates, which utilizes the polynomial approximation of arbitrary distributed loads to derive the analytical expressions of the stress function and stress components, and is therefore applicable to problems with a variety of loads. The analytical solutions of the wedge under continuous loads are obtained and verified with the results of the finite element method. The method is also applicable to the problem with piecewise continuous loads and discrete point loads in engineering practice. The corresponding comparison and verification of examples and the results of the finite element method are also shown.