This paper deals with joint stiffness off-line identification with new closed loop output error method which minimizes the quadratic error between the actual motor force/torque and the simulated one. The measurement of the joint position and its derivatives are not necessary. This method called DIDIM (Direct and Inverse Dynamic Identification Models) was previously validated on rigid robots and is now extended to a flexible joint manipulator. DIDIM method for flexible joint manipulators is derived into a three-step procedure: first, a rigid low frequency dynamic model is identified with DIDIM method; second, approximate values of the inertia ratio and stiffness are identified using the total inertia and friction values of step 1 and classical non linear programming algorithm; third, all the dynamic parameters (inertia, friction, stiffness) of the flexible robot are more accurately identified all together, starting from the values identified in step 1 and 2 and using the DIDIM method. An experimental setup exhibits results and shows the effectiveness of our approach compared with a classical output error methods.