Abstract: The characteristics for the cooperation system of flexible robot manipulators leads to that the mapping from driven torque space to generalized manipulation force space is not a single to single mapping, and this makes the manipulabiliy of such system more complicated. Based on the Finite Element Model of flexible robot, the relationships are established in present study among the balance torque of each driven joint generalized grasping force, corrected input quantity of each joint and generalized elastic displacement of the grasped payload. The outer boundary of generalized manipulation force is obtained for the first time by adding inequality constraints when the capacity of each driven joint is satisfied. A numerical simulation is also presented in the paper.