The research interest in flexible manipulators, lightweight and large dimension robotic manipulators, has increased significantly in recent years. Major advantages of flexible manipulators include small mass, fast motion, and large force to mass ratio, which are reflected directly in the reduced energy consumption, increased productivity, and enhanced payload capacity. Flexible manipulators have important application in space exploration, manufacturing automation, construction, mining, hazardous operation, and many other areas. In the present research, closed form equations of motion are derived for planar lightweight robot arm with two flexible link and revolute joints. The kinematics model is based on standard frame transformation matrices describing both rigid rotation and flexible displacement, under small deflection assumptions. The Lagrangian approach is used to drive the dynamic model of the manipulator robot. Links are modeled as Euler – Bernoulli beams with clamped – mass boundary conditions. The assumed modes method is adapted in order to obtain a finite – dimensional model. The associated eigenvalue problem is discussed and has been tried to obtain the exact dynamics model. Finally, a nonlinear control law has been proposed based lyaponove theory so that tip position of flexible arm track the certain trajectory, this control law has been developed to account uncertainty parameter and adaptive nonlinear control law has been proposed too. At last results of numerical simulation appears efficiently this method. The mathematical model of this two link flexible arm is derived by using the Maple and Matlab package and two assumed mode shapes for simulation has been used.