When a train goes round a curve, a transverse friction force may act at the contact points between the wheels and the rail in such a way that the wheels are excited to perform bending oscillations and to radiate a high–pitched squeal noise. This phenomenon has been modelled theoretically and simulated numerically. The wheel, which is a linear system, is described by a superposition of bending modes. It is excited transversely at one point along its edge by a stick–slip friction force, which depends nonlinearly on the wheel velocity. The growth rates of individual wheel modes are calculated, revealing the linearly unstable modes. The time history of the oscillation is also calculated, and this shows limit cycles dominated by the frequencies of some, but typically not all, of the linearly unstable wheel modes. Whether a mode is selected for the limit cycle depends on the time it takes for its velocity to reach a particular threshold and on its frequency relationship with other modes.