This paper deals with joint stiffness identification with new closed loop output error method which minimizes the quadratic error between the actual motor force/torque and the simulated one. This method called DIDIM (Direct and Inverse Identification Model) was previously validated on rigid robots and is now extended to a flexible joint manipulator. DIDIM method is derived into a three-step identification procedure: first, the rigid dynamic model is identified with DIDIM method; second, the inertia ratio and stiffness values are identified a first time, given the total inertia and friction of step 1, with a non linear programming algorithm; third, all dynamic parameters (inertia, stiffness, friction) of the flexible robot are more accurately identified all together a second time, starting from the values identified in step 1 and 2 and using DIDIM method. An experimental setup exhibits identification results and shows the effectiveness of this approach compared with a classical output error method.