Brake squeal results from friction-induced vibrations. This phenomenon is considered here and interpreted as a flutter instability of the steady sliding solution of an elastic solid in unilateral contact with friction with a moving obstacle. A mechanical analysis of the governing equations is given, in particular to obtain the steady sliding solution. The stability analysis of this solution is discussed. A numerical analysis by the finite element method is performed in order to compute the steady sliding solution and to discuss its stability for an automotive disk brake. The validation of the numerical procedure is examined in relation with some analytical results of the literature.