Revision with unchanged content. Brake squeal has been studied since 1930’s by many researchers through experimental, analytical and numerical methods in an attempt to understand, predict and prevent squeal occurrence. In recent years, the finite element (FE) method has become the preferred method in studying brake squeal. The popularity of finite element analysis (FEA) is due to the inadequacy of experimental methods in predicting squeal at early stage in the design process. However, the crux now lies in how the FE method can be a predictive tool rather than a diagnosis tool. This work proposes a new methodology of predicting squeal using the finite element method in order to produce a reliable predicted result. The advancement made in this work is consideration of a realistic brake surface topography. Comparison between complex eigenvalue analysis and dynamic transient analysis using a reduced FE model is also made for different contact schemes. Wear effects on instability of the disc brake assembly are also simulated. This book is suitable for those who are interested in brake noise and vibration issues like brake engineers, vehicle manufacturers, brake researchers, and undergraduate and postgraduate students.