In a horizontal rotating shaft containing a transverse crack, the vibration characteristics at the major critical speed are investigated. In a theoretical analysis, a model whose spring characteristic is approximately represented by a power series is treated. The analytic results are compared with the results of numerical simulation with a model of a piecewise linear spring characteristic. Experiments with a flexible rotating shaft system are also performed. The following points are clarified : ( a ) In the case of a comparatively large unbalance, the shape of resonance curves changes markedly depending on the relative angular position of the unbalance to the crack, and an unstable region appears for a certain range of angular position. This phenomenon is similar to the case of vertical shafts. ( b ) In the case of a comparatively small unbalance, the shape of resonance curves is not affected by the direction of the unbalance and an unstable region always appears. This is a phenomenon particular to the horizontal shaft.