An end thrust causes dynamic instability of flexible space structures. The sructure is modeled as a free-free uniform beam under a compressive follower force. The stabilization of the beam by means of an active control is investigated theoretically The control force is derived by the torque produced by a pair of tendons attached to the beam. The problem is solved by the Galerkin method in conjunction with the optimal regulator theory. The effects of the location. length and arm mass of the tendon on the stabilization of the beam are clarified through numerical simulation.