The mechanism of interfacial failure occurring as a consequence of the stress concentration induced by a matrix crack located in the vicinity of the interface is analysed. For this purpose, an asymptotic analysis is carried out to assess the competition between the propagation of the matrix crack towards the interface and the nucleation of an interfacial debond. An energetic approach provides a necessary condition comparing the ratio of the interfacial toughness over the matrix toughness to a critical value depending on the elastic mismatch between the fibre and the matrix and the ratio of the interfacial nucleation length over the width of the matrix ligament. Presented results show that the interfacial debonding is enhanced if the matrix is softer than the fibre. Further, a modified condition which does not involve the crack increment ratio is established if the matrix crack lies in the stiffest material.