A model to predict the effects of the accumulation of fibre breakages in unidirectional carbon fibre composites has been developed that takes into account several physical phenomena controlling fibre failure, including the stochastic nature of fibre strength, stress transfer between fibres due to the shear of the matrix, interfacial debonding and viscosity of the matrix. The damage processes leading up to failure are discussed and quantified, first in terms of fibre breaks for the case of monotonically increasing tensile loading, then for sustained loading and finally the implications for more complex loads and structures are discussed. It is clearly shown that the failure of a unidirectional composite structure results from the formation of random fibre breaks, which at high loads coalesce into clusters of broken fibres. Failure occurs suddenly with little warning in a sudden-death manner. The kinetics of fibre failure are different under steady loading, however, failure of the structure is still controlled by the viscoelastic nature of the matrix leading to the development of clusters of fibre breaks.