A new analytical method with sum function is introduced for solving plane problems of elasticity. The stress analysis of simply supported deep beam subjected to triangular distributed load has been performed. Furthermore, the Fourier series solution about above problems was given for the studied problem. The present method not only translates the coupling partial differential equations of elasticity into a few independent partial differential equation each other, but also the results using the present approach possess the same solution with those of traditional Airy stress function method. The correction and practical values was confirmed. The present method provides a more space of classical analytical method for solving the practical engineering problems.
