This paper eamines the damping effect of flywheel dampers installed at different shaft couplings on torsional oscillations on the 951 MW turbine-generator shafts due to network faults. A studied system is described and torsional fatigue on the turbine shafts following various electrical system disturbances is analyzed and evaluated. Moreover, the influence of the safety factor selected and set at the design stage to the shaft life expenditure due to fatigue damage is also presented. Useful additional insight into their modes of operation is obtained from the fast Fourier transform of the transient response results. All computer simulations thus show that the proposed dampers are effective in suppressing the torsional oscillations on the shafts. In this paper, time-domain torque evaluation is also combined with the fast Fourier transform method to derive a selection procedure for obtaining suitable flywheel dampers to depress the amplitude of these critical shaft oscillations to acceptable levels.