Matrix cracking bridged by intact fibres, which debond from the matrix and then slip against the matrix in friction, has been analysed for unidirectional fibre-reinforced ceramic composites under tensile loading parallel to the fibre axis. The effect of bonding at the fibre-matrix interface, Poisson’s effect of the fibre, and residualual stresses were included in the analysis. Both the crack-opening displacement and the displacement of the composite due to interfacial debonding have been analytically related to the fibre bridging stress. The critical stress for matrix cracking was also analysed. The existing solutions can be recovered by considering a special case in the present generalized solution.