Control of multiple robots, whose end-effects grasp an object, involves complex control tasks. First, the multiple robotic system, for a cooperative task, forms closed kinematic chains that impose additional kinematic and dynamic constraints. Second, the interactive actions among the robots through the object lead to the essential need to control position and interactive force, simultaneously. In this paper, the backstepping control method is studied for tracking control problem of cooperative robot manipulator system handling a common rigid object. The error system of coordinated robot manipulators is developed by defining the new variables based on the integral and differential of position and orientation errors. Then by defining the appropriate change of coordinates and using the backstepping design strategy, a backstepping position tracking control scheme is proposed for multi-robot manipulator systems handling a common object. Additional terms, using the properties of internal forces, are also added to the control signals to consider the force tracking problem. It is proved the closed loop system are uniformly ultimately bounded based on Lyapunov stability theory. Finally, the two three-link planar robot manipulators is applied for simulation, and the simulation results show the effectiveness of the proposed method.