The paper deals with friction induced vibrations and especially with railway disc brake squeal. The first part of the paper is devoted to the strategy used to model the general problem of self-excited vibrations of a rotating disc in frictional contact with two pads. Unilateral contact conditions with Coulomb friction and constant friction coefficient are considered. In order to predict the occurrence of self-excited vibrations, a classical stability analysis is performed, which consists on computing the complex modes associated to the linearised problem. A common interpretation of the stability analysis is that frequencies of unstable complex modes correspond to squeal frequencies. To check this assumption, the behaviour of the solution far from the sliding equilibrium is determined by using a non linear transient analysis. Moreover, an expansion of the transient solution on the complex modes provided by the stability analysis helps us to highlight the role of the unstable modes. The second part of the paper focuses on the application of the approach to the TGV disc brake system. Results on complex modes are presented and compared with measurements. The interest of both analyses is discussed.