Abstract: The nonlinear torsional vibration differential equation of a diesel shafting subjected to an impact force of expansion of vapour is established by means of Lagrange’s equation. According to the method of multiple scales for the nonlinear vibration the first approximate solution and the stability condition of primary parameter resonance of the system are obtained. The numerical analysis is carried out. The amplitude frequency response curves of the system are obtained. The Simulink simulation model of the system is established and the simulation is carried out. It is pointed out that primary parameter resonance of the system is in the stable state.