The mode of the mechanical torsional vibration system of the helicopter is not only easy to couple with the engine fuel conditioning system to produce self-excited vibration， but also resonance occurs when the natural frequency of the mechanical torsional vibration system and the frequency of the rotor excitation force are close to or coincide， so it is very important to calculate the frequency of the mechanical torsional vibration system. In this paper， the dynamic model of helicopter mechanical torsional vibration system is established by using the state space method. The frequency， damping ratio and time constant of a helicopter mechanical torsional vibration system are calculated， and compared with the first-order frequency of torsional vibration at 100% and 75% engine speed measured by the helicopter ground joint test-bed. The error is within the acceptable range of engineering application. The established state space model lays a foundation for the subsequent stability analysis combined with the mathematical model of engine and fuel control system.