The dynamic behaviour of structures - in particular, rotors containing cracks - is a subject of considerable current interest. Several researchers have developed models of cracked rotor systems considering mainly the transverse surface crack. In the present study finite element (FEM) analysis of a rotor-bearing system for flexural vibrations has been considered by including a shaft having a slant crack that has resulted from the fatigue of the shaft due to the torsional moment. A flexibility matrix for a slant crack and later the stiffness matrix of a slant cracked element have been developed to be used subsequently in the FEM analysis of the rotor-bearing system. The frequency spectrum of the steady state response of the cracked rotor was found to have sub-harmonic frequency components at an interval frequency corresponding to the torsional frequency, which can be used for crack detection. © 1997 Academic Press Limited.