Structural elements of steam turbines during operation are subjected to the intense mechanical and thermal loading in a corrosive environment. The consequence of such loads is the accumulation of fatigue damage with a risk of catastrophic destruction for the entire turbine. To detect damage in time a vibration diagnostics procedure based on changes in natural frequencies of rotors due to edge cracks at various orientations of crack relative to the axis of rotation at the stage of turbine repair is developed. The methods of vibration theory for the bodies with locally variable compliance caused by the crack were used. The influence of a crack on the rotor’s compliance was determined by the approaches of fracture mechanics. The effect of a surface transverse crack on the natural frequency of turbine rotor’s first mode shape at different orientations of the crack relative to the axis of rotation was determined, as well as the influence of crack location and the rigidity of the rotor on the sensitivity of natural frequency to the damage. The proposed method of damage detection in turbine rotors is sensitive enough to reveal relatively small cracks, the size of which does not pose a threat to the integrity of the rotor.