A new analytical model of chatter vibration in metal cutting is presented. The basic cutting mechanics adopted in the model is derived from a predictive machining theory based on a shear zone model of chip formation. A feature of this model is that variations of the undeformed chip thickness and rake angle due to the machine tool vibration are taken into account in determining the cutting forces and the forces are then coupled with the equations of motion to solve for the vibrational amplitudes with iterative techniques. Non-linearities in dynamic cutting processes caused by the effects of tool disengagement from the cut and cutting process damping are also included in the model. It is shown that the proposed model can be applied to make predictions for the suppression of chatter vibration by a change of tool geometries.