The current paper proposes a method to detect mechanical faults in rotating machines using three-phase electrical currents analysis. The proposed fault indicator relies on the use of instantaneous symmetrical components (ISCs), followed by a demodulation step enhancing the small modulations generated in electrical signals by mechanical faults. The limitations due to the multi-component nature of electrical signals, as well as to the noise naturally present in the measured signals are studied and taken into account in order to elaborate a proper and efficient algorithm to compute a mechanical fault indicator. It is theoretically shown that the ISCs based approach results in an increase of the signal-to-noise ratio compared to a single-phase approach, finally leading to an improvement of early fault detection capabilities. This result is validated using both synthetic and experimental signals where the proposed method is used to detect bearing faults and the obtained results are compared to single-phase results.