Brake squeal is a significant concern to automotive manufacturers because of noise-related customers’ warranty claims. Despite substantial research efforts in the past two decades, the reliable prediction of brake squeal propensity remains as challenging as ever. This is because brake squeal is essentially a nonlinear problem but the popular complex eigenvalue analysis (CEA) as a prediction tool is linear, while the material properties, operating conditions and friction behavior at the rotor-pad contact interface are not known accurately. In this thesis, the uncertainty analysis is used to improve the squeal prediction quality of the CEA. For an analytical friction oscillator with a nonlinear contact force, the CEA is found to under-predict instabilities compared to a nonlinear instability analysis. By incorporating uncertainties in the spring stiffness and friction coefficient, the under-prediction of the CEA has been significantly reduced although it increases with the strength of the nonlinearity. The friction oscillator is then extended to interconnected 3×3 friction oscillators model to consider uncertainties in friction modelling and contact area. Results show that frequently occurring unstable modes (ie, most likely to squeal) independent of friction models and contact area could be identified by the uncertainty analysis using CEA. Uncertainties in the lining surface roughness, material properties and friction are considered in the prediction of squeal propensity of a realistic disc brake using CEA on a finite element model updated by experimental modal testing results. While the deterministic model with a rough lining surface can predict some squeal frequencies identified in noise dynamometer tests, the deterministic model with a smooth lining surface is unable to predict any squeal frequencies. Yet, the uncertainty analysis can predict all squeal frequencies up to 10 kHz, hence superior to the deterministic approach, but there are still some over-predictions. A squeal index combining the occurrence of instability and normalised median net work can exclude most over-predictions. The uncertainty analysis shows that most of the original squeal frequencies could be eliminated by chamfered pads, validated by noise dynamometer tests. Analysis of the rotor-pad contact surfaces suggests that the reduction in squeal propensity is mainly due to the outer chamfered pad.