Abstract Process damping generated between the clearance face of the tool and wavy finish workpiece surface has a strong effect on cutting dynamics and stability. However, it has been mostly ignored in chatter analysis as there is hardly practical model for estimation of it, particularly for honed tool which equips arc cutting edge and performs significant process damping effect. The challenge of process damping modeling for cutting with honed tools lies mainly on the computation of the volume of the extruded material under the tool. In this study, based on the assumption of small amplitude vibrations, an analytical model with high computational efficiency is presented to compute the extruded volume in cutting with honed tools. Based on this model, we derive the equivalent process damping coefficient analytically by the energy dissipation principle and then construct the stability lobes by Full-Discretization Method. The predicted cutting stability is verified by previous researchers’ experiments and the existing process damping model. The results demonstrate that the proposed analytical method is applicable to deal with the problem of process damping for honed tool in milling operation.