A fault diagnosis method based on modal analysis is proposed to diagnose transformer core loose faults， and the resonant response of the transformer vibration signal and the natural frequency of the iron core can be used to identify transformer faults. The application of this method need to determine the natural frequency changing of transformer core with the loose core， this paper use ANSYS Workbench to determines the natural frequency of transformer core under different pre-tightening force， the change rule of combining experimental conditions before and after the acquisition of transformer core fault vibration signal， to verify the natural frequency of vibration signal and core resonant response can reflect the state of transformer faults effectively. The results show that the natural frequency of core decreases with the increase of looseness. The vibration signal and the natural frequency of the core are resonant with the 500 Hz component， and the amplitude of the signal increases significantly.