In order to improve the testing and design of filament wound composite structures a model to predict the accumulation of fibre breakages has been developed that takes into account all 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. In this, the first of three papers, the damage processes leading up to failure are discussed and quantified in terms of fibre breaks for the case of elastic monotonically tensile loading. 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. A critical damage state is found.