In this study a simple rectangular beam has been analyzed. For simplicity two dimensional plane strain problem is considered. The beam is fixed at the left and right edges of the bottom surface. Uniformly distributed load is applied along the length of the beam. A new formulation, known as displacement potential function formulation has been used here. Stresses and displacements at different sections along the length and depth of the beam have been plotted and discussed. The curves are found to be in complete conformity with the available literature and physical condition of the beam. The present literature reveals that the fixed connections of the beam are extremely critical regions and have the highest probability to fail.