The micromechanics of stress transfer has been analysed in a multiple-fibre composite which was subjected to uniaxial tension. The model composite was treated as a three-cylinder assemblage, which consisted of a central fibre, a matrix annulus and a composite medium. Analytical solutions have been derived for all major stress components for the composite with fully bonded fibre-matrix interface. A parametric study was performed on a carbon fibre-epoxy matrix composite. The result suggests that the principal effect of a stiff composite medium surrounding a discontinuous isolated fibre due to the high fibre volume fraction and stiff matrix, is to reduce the efficiency of stress transfer over the central potion of the fibre, while promoting the fibre-matrix interface shear stress concentration at the fibre end region. Practical implications of this observation with respect to fibre fragmentation and interfacial debonding are discussed.