Computer simulation of machining processes can save cost, time, and lead to reach an effective predictive capability. In this paper, by using computer simulation, damping capability of the lathe tools under static and vibrational analysis at different tool overhang conditions is studied. A novel predictive model of the cutting tool is developed, in which damping capability of the tool is improved by using composite material with high damping capability. Epoxy granites with normal, rigid, and plastic structures were used as composite materials in modified model of tool holder. The all-metal model, model with holes in tool holder and the modified model filled up with the composite material, with the same geometry and dimensions are used.