In order to find some way to detect a transverse crack due to fatigue in a rotating machine, we have investigated experimentally and theoretically the change in the resonance curve caused by the occurrence of a crack. The experimental apparatus is a vertical rotating shaft system where an elastic shaft with a disk is supported simply at both ends. In the experiments, the amplitude curve and phase angle curve were measured in the neighborhood of the major critical speed for various angular positions of unbalance. The results show that the shape of the resonance curve changes extremely due to the direction of the unbalance, and an unstable region appears when the unbalance exists in the same direction as the crack. It is shown that this phenomenon is explained theoretically by combining the characteristics of the unsymmetrical shaft and those of the symmetrical shaft and those of the symmetrical shaft or by considering rotating nonlinear spring characteristics.