Activation theory used in metals and polymers has been used to model creep of unidirectional composite and resin matrix, using the concept of internal stress. The model fits the experimental creep curves very well for a range of materials. The results obtained for a brittle epoxy and its carbon fibre-reinforced composite with two fibre orientations are reported. The model parameters, such as internal stress, activation volume and activation energy, have been measured experimentally and compared with model-fit values, and their influence on creep is discussed. Finally, an approach to predict the creep rupture of unidirectional composites using internal stress is presented.