This paper deals with the dynamic identification of the Kuka LightWeight Robot LWR4+. Although this robot is widely used for research purposes by many laboratories, there is not yet a published dynamic model available for model based control or simulation. Because Kuka does not give any information about the dynamic parameters of the robot we propose to identify 2 sets of parameters using the usual off-line identification method which is based on the Inverse Dynamic Identification Model and linear Least Squares technique (IDIM-LS). The first set is obtained by the actual dynamic parameters of links and joints (inertia, gravity and friction parameters) which are identified from motor torques and motor positions data. The second set is obtained by the Kuka's inertial parameters of links, implemented in the controller for model-based control. This is a reverse engineering procedure which recovers the confidential manufacturer's data. The link parameters are estimated using the IDIM-LS method with the sampled data of the inertia matrix and the gravity torques computed by the controller. To complete the reverse engineering procedure we also identify the joint stiffness parameters used by Kuka to estimate the joint link side position using the joint torque sensors and motor positions data. A Comparison between the actual dynamic parameters and the Kuka's parameters allow concluding to a reliable data sheet. This is a strong and very useful result for future work of the scientific community on this very popular robot.