In this paper, a mathematical model has been developed for the cutting tool stresses in machining of nickel-based super alloy Inconel 718 used in aircraft and spacecraft industries, nuclear power systems and steam generators etc. necessitating oxidation and corrosion resistance, high temperature and strength. The cutting forces were measured by a series of experimental measurements and stress distributions on the cutting tool were analyzed by means of the finite element method using Ansys software. The mathematical modeling process of the compressive stresses in x, y and z directions was carried out with multiple regression analysis regarding to Ansys stress results depending on the cutting forces and the chip–tool contact area. It is found that model results had good agreement with the Ansys stress results.