This article presents a systematic approach for identifying the Cartesian stiffness of a 5-degree-of-freedom (DOF) hybrid robot for machining that includes a parallel mechanism and an A/C wrist. The novelty of this approach is that the elasticities of both links and joints in the parallel mechanism are integrated into the compliance (inverse of stiffness) parameters at the limb level. By identifying the compliance parameters at the limb level rather than at the joint/link level, the number of parameters to be identified is significantly reduced and the complexity of the identification problem is decreased. Based on screw theory, the Cartesian stiffness model of this hybrid robot is established first. Then, by reconstructing this stiffness model, a linear regression model suitable for estimating the compliance parameter is derived. In addition, a two-step systematic procedure for parameter estimation is introduced, including the reconstruction of the design matrix and robust ridge estimation. Finally, both computer simulations and experiments are carried out to demonstrate the validity of the proposed approach. The simulation results show that the predictive deviations of the end-effector deflections identified by ridge estimation are less than those estimated by linear least squares, confirming its greater robustness. The experimental results indicate that the developed method has potential in industrial settings.