Abstract: Chatter is an undesired phenomenon of self excited vibrations that occurs during many machining operations. This paper analyzes mode coupling chatter from the point of view of the system theory. A simplified mathematical model of the cutting process is established, from which the equations of the system are obtained. Then, the eigenvalues and the eigenvectors of the system are evaluated, and a simple stability condition is formulated. The tool trajectories both in the stable and unstable case are studied. Finally, an example of mode coupling chatter in a machine for wood cutting and its stabilization are presented.