Abstract: A semi-inverse method from stress functions is used to obtain elasticity solutions of a simply supported beam with different modulus under uniformly distributed load and its approximate solutions derived from mechanics of material are also checked. The results show that because the materials with different modulus are employed, the stress redistributes across section in a large extent and the maximum normal stress obtained from mechanics of materials is underestimated to a certain degree. These errors fluctuate according to different modulus of materials and enlarge especially in the case of deep beams.