Turbine Blades suffer fatigue damage when they cross over a critical speed during start up and shut down conditions. The stress response is usually determined from quasi-steady analysis through resonance with an assumed damping. This response above fatigue limit can be divided into several steps to reach the peak value at critical speed and then fall after passing the critical. For a given acceleration of the rotor, one can then determine the number of cycles at each of these stress levels and assess cumulative damage for one crossing. In this paper, the effect of acceleration and damping on the magnitude of peak stress and where it occurs in the vicinity of critical speed is included in determining the damage suffered by a blade while passing through the critical speed.