The eccentricity in induction machines is a geometrical fault when the axis of rotation deviates from the ideal. As a result, the air gap between the stator and the rotor varies. Since the eccentricity is caused by a geometric misalignment, finite element method is used to model the fault in this paper and the phenomenon is detected by spectral analysis of the stator currents. In addition, the effect of eccentricity on the controlled drive is also investigated by numerical simulations.