This paper presents a method for the diagnosis of induction machines faults. The proposed method is capable to detect the presence of both dynamic eccentricity and broken rotor bar faults. Several studies have attempted to model an induction machine with isolated faults and provide methods for detecting them. However, the challenge begins, with the occurrence of combined defects which produce fault signatures that are difficult to separate. The novel proposed method is based on the measured air-gap magnetic flux density spectrum, which allows for the detection of combined faults. A finite element method is used for modelling the induction machine under faulty conditions, where the faults of rotor bars are created by a deleting operation of the boundary condition which is added to the air-gap part. Then, the dynamic eccentricity is formed by the movements of the rotating rotor’s centre with different ratings. From a modelling perspective, the contribution of the current work is the establishment of the relation of the air-gap of the rotor for modelling this kind of eccentricity fault. In addition, the proposed model of the air-gap includes two parts; one related to the stator and another one to the rotor, called statoric air-gap and rotoric air-gap respectively. The rotoric air-gap is employed for the dynamic eccentricity modelling. Computer simulations are presented using the air-gap magnetic vector and the magnetic field in X and Y components, to confirm the robustness of the proposed technique. Finally, the air-gap magnetic flux density spectrum is used for the analysis of combined rotor faults.