A modified inclusion model for matrix cracking in a fiber-reinforced brittle-matrix composite is proposed. The bonding energy of the fiber-matrix interfaces and the residual stresses are included in the present model. Special attention is paid to long cracks (steady-state cracks). The parameter κ is found to distinguish the case of complete bridging (perfectly bonded interfaces) and that of slipping fibers. Moreover, the theoretical prediction of the critical applied stress σ A c is compared with that of the BHE model and experimental data. Finally, the optimal value of the fiber volume fraction is investigated for a composite with residual tension in the matrix.