A spindle apparatus comprises a main shaft mounted for rotary movement, a rotating device for rotating the main shaft about an axis, a vibration device for vibrating the main shaft, a detecting device for detecting a displacement of the main shaft when the main shaft is vibrated by the vibration device and providing an output signal indicative of the displacement of the main shaft, a calculating device for calculating an allowable revolution speed of the main shaft on the basis of the output signal of the detecting device, and a drive source for driving the rotating device to rotate the main shaft within a speed range which does not exceed the allowable revolution speed. When an end of the main shaft is vibrated by the vibration device, a displacement of the vibrated main shaft is detected by the detecting device which provides an output signal indicative of the detected displacement. The calculating device calculates an allowable revolution speed of the main shaft on the basis of the output signal of the detecting device and outputs the calculated allowable revolution speed to the drive source. The drive source drives the rotating device to rotate the main shaft within a speed range which does not exceed the allowable revolution speed.