The current article presents an analytical approach, for determining the natural frequencies of a rotating cracked Euler–Bernoulli beam with a varying transverse cross-section, using the so-called differential transform method (DTM). First, the natural frequencies of the beam are obtained for different values of the crack position and depth. The results have been validated against those obtained from experimental modal test, Abaqus software and some other methods reported in the literature and a good agreement between the results is observed. Then, the inverse problem is investigated. For this reason, the position and depth of the crack of the rotating beam with a varying transverse cross-section are estimated using the genetic algorithm and then, the natural frequencies are obtained from the modal test. It is seen that the numerical results have a suitable agreement with the actual position and depth of the crack that indicates the effectiveness of this method in determining the parameters of the crack in the rotating beams.