Abstract : Brake squeal is a common noise problem encountered in the automotive industry. Higher friction coefficients and weight reduction recently led to higher vibration levels in the audible frequency range. This quality issue becomes economic due to penalties imposed to the brake supplier although no robust design method exists. The industrial practice thus relies on costly prototyping and adjustment phases. The evolution of computational power allows computation of large mechanical assemblies, but non-linear time simulations generally remain out of reach. In this context, the thesis objective is to provide numerical tools for squeal resolution at early design stages. Parameterized reduction methods are developed, using system real modes as Rayleigh-Ritz vectors, and allow very compact reduced models with exact real modes. The proposed Component Mode Tuning method uses the components free/free modes as explicit degrees of freedom. This allows very quick sensitivity computation and reanalyzes of an assembly as function of local component-wise parameters. Non-linear time simulations are made possible through two ingredients. A modified non-linear implicit Newmark scheme and a ﬁxed Jacobian are adapted for contact vibrations. The brake is reduced keeping a superelement with exact real modes and a local non-linear ﬁnite element model in the vicinity of the pad/disc interaction. A set of design tools is illustrated for a full industrial brake model. First, instant stability computations and complex mode trajectories are studied. Modal interactions and non-linear phenomena inside the limit cycles are thus well understood. Time/frequency correlations are performed using transient modal identiﬁcation and space-time decomposition. A time domain modal damping model is also shown to be very useful. The modiﬁcation of a critical component for squeal resolution is ﬁnally tested and validated.