Electrical rotating machines are often system-relevant in their application. To avoid unplanned failures, the machines are regularly checked for faults. A novel way to do this is the SFRA method. It is non-invasive and can be carried out with little effort and short measurement time. Furthermore, it is possible to detect different faults in the magnetic or electrical circuit simultaneously. The main objective of the present paper is to give the theoretical background for this new application. For this purpose, empirical measurements are carried out on fifteen different synchronous machines and induction machines. The power classes and designs are very different and thus provide important information on the transferability of the measurements. A generally valid trace, consisting of four frequency ranges, is developed. This is used for verification of the developed gray box model. Important influences such as the neighboring phases and the actual position of the rotor are taken into account. A periodically repeating behavior as a function of the number of pole pairs is shown, which can only be observed in certain frequency ranges. This periodicity must be taken into account in reference measurements. The influence of the neighboring phases overlaps the main resonance of the measured phase. A second resonance point is formed in a similar frequency range. Finally, three examples for fault detection are given. Short circuit faults are investigated using an induction machine stator. Even a single shorted turn is already changing the frequency response. Ground faults have a greater effect on SFRA measurements. Due to the additional conducting path to ground within the winding, the initial damping becomes larger. The remaining frequency ranges are also strongly influenced by this fault type. A fault that is usually difficult to detect is the rod rupture in the damper cage of synchronous machines. With the help of SFRA measurements, this fault can be detected via the periodicity even without a reference measurement. In summary, it is shown that short circuits, ground faults and rod ruptures in the damper cage can be detected with the method.