The generalized plane strain (GPS) linear elasticity model is considered. The displacement field U has three components U 1, U 2 and U 3 depending only on two space variables x 1 and x 2. In such a framework, the interface is a plane surface spaned by x 1 and x 3 and the interface crack front is a straight line parallel to x 3 (figure 1). It is implicitely assumed that the crack front ends are sufficiently far away to be ignored and then this model allows to study the three dimensional elastic fields in a vicinity of any interior point of the crack front. It embeds, as particular cases, the bidimensional plane strain model and the anti-plane scalar problem.