Squeal noise has been an on-going concern with automotive brake systems since their inception. Even after many decades of research no single theory exists that adequately describes the phenomenon, and no general methods for eliminating squeal noise exist. Broadly speaking, three primary methods of analysis have been applied to understanding and eliminating brake squeal: analytical, experimental and numerical. Analytical models provide some insight into the mechanisms involved when a brake squeals, but have limitations in applicability to specific brake systems. Experimental methods provide the backbone of brake squeal investigations, especially in an industrial environment. However, the core focus of this thesis is to use a large scale finite element analysis (FEA) model to investigate brake squeal. Initially the FEA model was developed and the dynamic characteristics were validated against experimental modal analysis results. A complex eigenvalue analysis was performed to identify potential squeal modes which appear as unstable system vibration modes. Further techniques are described that allow the deeper probing of unstable brake system modes. Feed-in energy, which is the conversion of friction work into vibrational energy during the onset of squeal, is used to determine the relative contribution of each brake pad to the overall system vibration. The distribution of the feed-in energy across the face of a brake pad is also calculated. Component strain energy distributions are determined for a brake system as a guide to identifying which components might best be modified in addressing an unstable system mode. Finally modal participation is assessed by calculating the Modal Assurance Criterion (MAC) between component free modes and the component in the assembly during squeal. This allows participating modes to be visualised and aids in the development of countermeasures. The majority of the work in this thesis was performed using the commercial FEA code MSC.Nastran with user defined friction interfaces. An alternative approach using a contact element formulation available in Abaqus was also implemented and compared to the MSC.Nastran results. This analysis showed that considerable differences were noted in the results even though the overall predicted stability correlated relatively well to observed squeal. Abaqus was also used in a case study into the design of a brake rotor in a noisy brake system. The results of this study provided good correlation to observed squeal and facilitated effective rotor countermeasures to be developed. Some success was achieved in the main aims of predicting brake squeal and developing countermeasures. However, while the tools presented do allow a deeper probing of system behaviour during squeal, their use requires good correlation to observed squeal on brake system to be established. As such, their use as up-front design tools is still limited. This shortcoming stems from the complexity of brake squeal itself and the limitations in modelling the true nature of the non-linearities within a brake system.