Abstract: A multi-degree system consisting of workpiece and cutting tool elastic subsystems is studied. A model for the system under the action of nonlinear dynamic cutting force is established. The internal resonance phenomenon is analysed using numerical methods. Results show that the amplitudes of the two subsystems influence mutually and increase sharply. The analytical solutions of 1:2 internal resonance are obtained using KBM methods, and a group of stable amplitude curves of the two subsystems are gained. The conditions of cutting chatter occurring in this vibrating system are also discussed through analysing the resonance curves.