It is natural to suppose that some of the technological factors associated to the processes used in the fabrication of metal matrix composite (MMC) materials can and will influence in some extent the performance of these materials when in service. This is often true due to the levels of residual stresses that may be induced in the MMC after the cooling down phase during the fabrication process. In the present work, the authors propose a complete three-dimensional constitutive model and numerical implementation procedure that allows the determination of residual stress fields in metal matrix composites. The model is based in a thermoelastic reinforcement behaviour and a thermoelastic-viscoplastic matrix behaviour. The role of the reinforcement volume fraction and cooling rate on the levels of residual stresses at room temperature is investigated with the proposed model. For this purpose, a large set of simulations is performed with Al-SiC metal matrix composites. Two different unit cells are used, representative of continuous and short fiber reinforcement MMCs. The tested reinforcement volume fractions range from 5% to 35% and cooling rates from 0.1 to 500 K s. The influence of these parameters is evaluated in terms of the resulting stress fields at room temperature. It is shown that the levels of equivalent stress can reach values above the yield limit of the aluminium matrix, leading to plastic straining near the matrix/reinforcement interface.