In the practice of metal treatment by cutting it is frequently necessary to deal with self-excited oscillations of the cutting tool, treated detail and units of the machine tool. In this paper are presented differential equations with the delay of self-excited oscillations. The linear analysis is performed by the method of D-expansion. There is chosen an area of asymptotically stability and area D2. It is prove that, in the area D2 the stable periodical solution appears. The non-linear analysis is performed by the theory of bifurcation. The computational experiment of metal cutting process and results of these experiments are presented.