This research is devoted to statics analysis of structural members under mechanical loads. Static analysis of beams under uniform transverse mechanical loads is presented. The beams are supported by simply supported boundary condition at both sides. The equilibrium equation of the beams is obtained and solved using analytical method and numerical method. The numerical method employed in this work is generalized differential quadrature (GDQ) method. The type of differential quadrature method used for numerical solution is the polynomial-based GDQ method. The differential equation is discretized into algebraic equations based on the GDQ technique. The algebraic equations are then solved to obtain the deflections of the beam. The results of GDQ method are compared with the analytical solutions. It is found that the result of GDQ method are in good agreement with those of analytical solution which shows high accuracy of the GDQ method. Effects of material properties, geometrical property (cross section of beam), and mechanical loads on deflection of the beams is investigated.