Research interest in flexible manipulators, lightweight and large length robotic manipulators, has increased significantly in recent years. According to recent advances in using robots and human need to them with high speed and excellent quality, the analysis flexible robot is objective. The objective of the flexible robot design is to reach fast motion and high maneuverability compared to slow motion of rigid industrial robots. 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. Many robotic applications involve interaction of the robot with its environment. In many of these applications, the environment is an object to be manipulated or a work piece to be machined. The contact of a robot with an environment will lead to impact if the robot end-effector has a nonzero normal velocity component at the point of contact. When contact occurs, impact dynamics can be a significant factor. If impact forces are not modeled, and if the movements of the manipulator are not controlled to prevent inappropriate forces, the robot operations may fail. Impact often occurs when a robot contacts the environment with its end-effector(s). During impact the robot motion is interrupted and impulsive forces develop at the contact point(s) and at each joint. A quantitative relation between the impulses and other dynamic parameters will help analyze the severity of the collision and design reliable robotic systems. In this thesis using the Lagrange approach and impact theory, behavior of flexible-joint robots and the flexible-link robots in collision with environment, is investigated. Flexibility of each flexible joint is modeled as a linearly elastic torsional spring and equation of motion for robot is obtained by Lagrange approach. The flexible-link robot equation of motion is obtained using the Lagrange approach and the 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 mathematical model of two flexible-link manipulator is derived by using one assumed mode shapes. Common methods of measuring impulse force use sensors to determine the magnitude of the impulse force applied to the system. In this thesis the impulse force is obtained using some common impact assumptions and Lagrange approach. After integrating Lagrange equation and combining with callasical theoery,impulse force is determined as a function of system parameters and its effect on the robot system is studies. keywords: Impact, Flexible robot,Lagrange approach, Impulse force, Simulation