Polynomial beam model is used in the present research study to determine the deflections of functionally graded beams under uniformly distributed loading. This hypothesis is formulated using the principle of virtual work. A polynomial beam theory was used to compare the deformations of functionally graded (FG) beam loaded uniformly. This polynomial beam theory ascertains the traction-free conditions on the both top and bottom ends of the beam. The FG beam is treated as a simple supported beam. Hence, Navier’s solution is employed to develop governing equations. The numerical results were then compared with existing theories in the literature and found to be consistent with the current theory.