This article focuses on nonlinear vibrations of a workpiece during the turning process. Applying numerical methods, the two degree of freedom model has been analysed. A cutting force possesses two kinds of nonlinearities. One of them is connected with the depth of the cut and the other results from a relative velocity between a tool and a chip. The cutting force acting on the workpiece causes a displacement of workpiece symmetry axis relative to the rotation axis. It produces an appearance of an additional inertia force, which can be essential during high rotational speed.