Condition based maintenance systems (CBM) of induction machines (IMs) require fast and accurate models that can reproduce the fault related harmonics generated by different kinds of faults, in order to help in developing new diagnostic algorithms for detecting the faults at an early stage, to analyse the physical interactions between simultaneous faults of different types, or to train expert systems that can supervise and identify these faults in an autonomous way. To achieve these goals, such models must take into account the space harmonics of the air gap magnetomotive force (MMF) generated by the machine windings under fault conditions, due to the complex interactions between spatial and time harmonics in a faulty machine. One of the most common faults in induction machines is the rotor eccentricity, which can cause significant radial forces and, in extreme cases, produce destructive rotor-stator rub. But the development of a fast, analytic model of the eccentric IM is a challenging task, due to the nonuniformity of the air gap. In this paper, a new method is proposed to obtain such a fast model. This method, which is theoretically justified, enables a fast calculation of the self and mutual inductances of the stator and rotor phases for every rotor position. The proposed method is validated first using a finite elements method (FEM) model, and then, through an experimental test-bed using commercial induction motors with a forced mixed eccentricity fault.