Recent developments in the holographic investigations of brake noise have produced a wealth of information concerning the vibrations of disc brake systems when high frequency noise (squeal) is being generated. Accurate measurements of the amplitude and phase of the 3D surface displacements of the disc rotor vibrations have been obtained. As well as finding the main frequency(s) and mode of vibration it has been possible to study features such as the in-plane components of the displacement of the disc rotor (often significantly large) and travelling waves moving round the disc at a speed dependent on the frequency and mode order of the vibrations but independent of disc rotational speed. Examining mathematical models that employ a distributed parameter approach (i.e. using a partial differential equation or systems of partial differential equations) to represent disc brake systems, this paper considers the use of numerical methods that are very efficient in computation time. Such methods - known generically as spectral and pseudo-spectral methods - can be used to produce animated solutions of the equations. Thus the parameters used in the models can be easily varied and the partial differential equation(s) solutions compared to the above observed features.