Deflection of a matrix crack at the fiber/matrix interface is the initial mechanism required for obtaining enhanced toughness in ceramic-matrix composites (CMCs). Here, energy, release rates are calculated for matrix cracks that either deflect or penetrate at the interface of an axisymmetric composite as a function of elastic mismatch, fiber volume fraction, and length of the deflected or penetrated crack. The energy release rates for the competing fracture modes are calculated numerically by means of the axisymmetric damage model developed by Pagano, which utilizes Reissner's variational principle and an assumed stress field to solve the appropriate boundary value problems. Crack deflection versus penetration is predicted by using an energy criterion analogous to that developed by He anti Hutchinson. Results show that, for equal crack extensions in deflection and penetration, crack deflection is more difficult for finite crack extension and finite fiber volume fraction than in the He and Hutchinson limit of zero volume fraction and/or infinitesimal crack extension. Allowing for different crack extensions for the deflected and penetrating cracks is shown to have a small effect at larger volume fractions. Fracture-mode data on model composites with well-established constitutive properties show penetration into the fibers (brittle behavior), as predicted by the present criteria for crack extensions larger than 0.2% of the fiber radius and in contrast to the He and Hutchinson criterion, which predicts crack deflection. This result suggests that the latter criterion may over-estimate the prospects for crack deflection in composites with realistic fiber volume fi actions and high ratios of fiber to matrix elastic modulus. (C) 1998 Elsevier Science Ltd. All rights reserved.