Introduces a cutting dynamic model considering process damping and its analytical solution to the cutting stability. Applies the developed simulation program to simulate and analyze the stability of turning and milling operations respectively, and the cutting tests verify the correctness of the proposed model and the simulated program. Compares the cutting stability lobe diagram with and without considering process damping, and finds that the stability limit is improved remarkably at low cutting speeds when the effect of process damping is considered. The cutting stability simulation approach considering process damping is applicable for high efficiency cutting of aeronautical hard-to-machine materials.