We investigated and modelled the process of ultrasonic extrusion of a thread when imposing the ultrasonic oscillations. Based on the rheological model of deformation of the perfect elastic-plastic body, we constructed dependences for the calculation of contact pressures and specific friction force. In carrying out the present research, in order to simplify a mathematical model, the assumption was made on that the phenomenon of surface strengthening exerts little effect on the magnitude of contact pressure and friction force at plastic deformation. This mathematical model describes complex motion of the tool (rotational and oscillatory motion of the tap). The system of the derived dependences, which describes the influence of oscillation amplitude, oscillation direction, deformation rate, and mechanical properties of the machined material on the magnitude of contact pressure, makes it possible to estimate parameters of the process of plastic deformation when imposing the ultrasound. By employing such a description, it is possible to derive the value of contact pressure and friction forces for each region of the load chart. During analysis of the obtained results it was established that an increase in the amplitude of oscillations leads to a decrease in the time of contact between a tool and the machined surface, which is why contact pressure, specific friction of axial and torsional oscillations over a period decrease accordingly within a change in the examined factors. The benefit of the present study is a detailed analysis of the contact interaction between a tool and a part, as well as consideration of mechanical properties of the machined material, which makes it possible to choose the modes of treatment and to provide maximum operational performance