Metal cutting is a complex process in which several mechanisms are at work simultaneously. The mathematical modelling allows carrying out research into the optimization of machining conditions. This work examines the simulation of chip formation during the process of cutting. The studies demonstrated that the chip formation process, taking into account the plastic deformation and destruction of metal in the local zone, is most appropriately represented by a rheological model in the form of a series connection of elasticductile- plastic relaxing medium of Ishlinskiy (reflecting the process of primary deformation of metal from the cut off layer) and the medium of Voigt with two elastic-dissipative elements (representing the process of deformation and frictions from the convergent shaving). The attained complex rheological model served as the basis for constructing a representative dynamic model for the chip formation process. The key factors that govern the chip formation have been taken into account, such as tool vibration frequency and amplitude, depth of cut, feed rate.