The coupled criterion predicts crack nucleation at a stress concentration point. It is a twofold criterion that uses conditions for energy and tensile stress and involves both the toughness and tensile strength of the material. In general, the crack jumps a finite length and then either stops or goes on growing. The criterion has proven its effectiveness in many situations encountered in homogeneous materials like V- and U-notches and predictions agree reasonably with experimental measurements. It can also be used to study specific mechanisms of degradation of composites such as delamination or fibre debonding. It has recently been used successfully to predict the initiation of delamination from a stress-free edge; the application discussed in this chapter is the deflection of transverse cracks by an interface. However, it is valid for both delamination between layers and fibre debonding.