Future power system faces several challenges; one of them is the high penetration level of intermittent wind power generation, which provide small or even no inertia response, not contributing to the frequency stability. In this paper, the effect of the shaft stiffness on the inertial response of the fixed speed wind turbines and its contribution to the system inertia is presented. Four different drivetrain models based on the Multi-body System are presented in this paper. The small-signal analysis of them demonstrated no significant difference between models in terms of electro-mechanical eigen-values for increasing of shaft stiffness. The natural resonance frequency of the torsional modes of the drivetrain show slightly different values between damped and undapmped models but not significant differences are found in the number-mass model. Time-domain simulations show the changes in the active power contribution of a wind farm based on fixed speed wind turbine during system frequency disturbance. The changes in the kinetic energy during the dynamic process have been calculated and their contribution to the inertia constant has been found small but effective. The largest contribution of the kinetic energy is provided at the very beginning of the system frequency disturbance helping to reduce the Rate of Change of Frequency, which is positive for the frequency stability.