The study of the stresses implied on a flexible robotic arm as a major contributing factor in determining the deflection of these manipulators is a proper step for the rule-based system determining the most convenient payload the arm can bear. This work suggests a dynamic system for a robotic flexible arm pivoting around a hinge. The Lagrangian dynamics equations are used to derive its equations of motion. The model describes the global motion of the single-link flexible manipulator as a large motion and small motion. The solution to these equations were effected using the Rung-Kutta method to produce the response for the flexible arm to a step input torques, all together with the study of the effect of payloads on the arm response. The results obtained have shown that the ram deviation becomes unstable with the increasing of payloads