A nonlinear, two degree of freedom numerical chatter vibration analysis of metal cutting is presented. A new angle relationship is proposed. The model takes into account nonlinearities such as fluctuation of the friction coefficient on the tool-chip interface, oscillations of cutting force amplitude and direction, separation of the tool edge from the material and cutting process damping. The effects of shear-angle fluctuation, cutting speed variation and mode angle on stability are also included in the model. Numerical solutions of the governing dynamic equations are obtained and the model is tested by comparing the results of computer simulations of orthogonal wave cutting and wave removing processes to the existing experimental data. Curves of calculated tool displacement, shear angle, friction coefficient and cutting forces are given. Generally good agreement is observed between the theoretical results and the existing experimental data.