In the present study a simple Laval rotor with a transverse crack is considered. The analysis assumes that the vibrations remain small in comparison to the sag of the rotor under its own weight. If a cracked shaft rotates slowly under the load of its own weight, then the crack will open and close once per revolution, i.e. it breathes. Considering a simple hinge model which is a very good model for small cracks with the breathing action of crack, the transient vibration response of a cracked rotor passing through its critical speed is analysed, as an attempt for crack detection and monitoring. Effects of different factors such as crack depth, unbalance eccentricity with phase and acceleration influencing vibration are investigated. © 1998 Elsevier Science Ltd. All rights reserved.