Stress is transferred to the fibres in a fibrous composite material through interactions at the fibre surface. A number of descriptions of different transfer processes have been developed but these give little information on the state of stress within the fibre itself. The analysis presented here enables the internal stresses and strains generated within the fibre by the different stress transfer mechanisms to be analysed. The results show clearly different stress patterns for the mechanisms studied; fibres in a plastic or metallic matrix compared with those in an elastic matrix. The definition of a 'critical length' in the latter case is not so clear as is sometimes suggested.