A model of chip formation with a single conditional shear surface cannot be implemented in determining the stresses and strains in the blank and chip neither nor in determining the contact stresses at the working sections of the front and read cutter surfaces. At the same time, it has been established experimentally that the cut layer is converted to chip in a plastic zone of complex form. Numerous attempts have been made to simulate this zone by constructing slip-line fields. According to plasticity theory, slip lines constitute two families of mutually orthogonal curvilinear coordinates, along which the maximum tangential stress acts. If the kinematically possible slip-line field is constructed, it is possible to calculate the stress-strain state in the chip-formation zone.