The article presents an approach to detecting and locating internal short-circuit faults through analyzing the frequency responses of transformer windings. The proposed approach is based on estimating changes in the winding natural frequencies and presenting them in the form of graphic images (patterns). The results from investigations of the physical and mathematical models of windings are given, which show the characteristic patterns of changes in the natural frequencies depending on the location of disk-to-disk and turn-to-turn short-circuit faults along the winding height. Approaches to locating an inner fault in a winding using a graphic method and using the obtained empirical expressions are presented.