Abstract: The coupled vibrations of rotor with different type of cracks were studied, including transverse crack, transverse-slant crack and arbitrary slant crack. It aims to reveal the variation rule of stiffness parameters in different directions, their cross-coupling mechanism and especially the feature of resulted vibrations of the cracked rotor. The rotor segment with different type of cracks, including transverse crack, transverse-slant crack and arbitrary slant crack, was respectively modeled using the Timoshenko beam element, considering all six degrees of freedom including longitudinal, bending and torsional directions. Flexibility coefficients and then stiffness matrix was derived, based on strain energy theory. On this basis, motion equation of the cracked rotor was solved by numerical algorithm `Newmark-beta' to obtain the time-domain response of coupled vibrations of the cracked rotor under different excitations by single or multiple faults such as unbalanced excitation, torsional excitation and combined excitation of unbalanced with torsional. The spectral characteristics of coupled vibrations were then analyzed. Compared to either transverse crack or transverse-slant crack, the stiffness matrix governed by arbitrary slant crack is more populated with additional cross coupled coefficients, and its cross coupling effect is more significant, which contributes to stronger coupled vibrations in bending-torsional direction or even longitudinal-bending-torsional direction. The amplitudes of both bending vibration and torsional vibration are larger than that at the situation of either transverse crack or transverse-slant crack, under the action of either unbalanced excitation or torsional excitation. Moreover, the characteristic frequencies of coupled vibrations of rotor with different type of cracks including transverse crack, transverse-slant crack and arbitrary slant crack, are of different sensitivities to oriented angle of crack surface, for example the rotating fundamental frequency and its second harmonic frequency, the torsional excitation frequency and its sideband components. These research results can provide theoretical basis for both characteristic parameters identification and diagnosis of rotor cracks.