A mathematical model is presented for the squeal noise generated by trains when traversing tight curves. Curve squeal is presumed to arise from lateral crabbing of the wheels across the rail head. This induces a lateral friction force acting at the contact of each wheel with the rail. An individual wheel the performs out-of-plane oscillations which are radiated and heard as squeal. This phenomenon is modelled by considering a flat round disc, with several out-of-plane modes, excited at one point along the edge by a dry-friction force (typically a stick/slip force) which is dependent on the disc velocity. An iteration scheme is developed which gives the time history of the disc velocity. The iteration is straightforward and only requires the impulse response (or the Green's function) of the disc and the functional dependence between friction force and disc velocity (friction characteristic). The numerical simulations produce time histories that show transient phenomena, such as exponential amplitude growth and the onset of limit cycles. The way these phenomena are influenced by some parameters, in particular the modal loss factors of the disc and its crabbing speed, will be examined. Practical methods to reduce or eliminate curve squeal will be discussed.