There are a number of approaches reported in the literature for modelling cracks in shafts. Although two and three dimensional finite element models may be used, the most popular approaches are based on beam models. Of particular concern is the modelling of breathing cracks, which open and close as the rotor spins due to its self-weight. One simple model of a breathing crack assumes the shaft stiffness varies as a cosine function as the crack opens and closes. In large rotating machines the deflection caused by out-of-balance forces is small compared with that due to gravity and also the cracks are, at least initially, small. This paper will consider the influence of these two assumptions on the response of a cracked Jeffcott rotor. The effect of an asymmetric shaft is also considered.