In this chapter, a delamination in a multi-directional (MD) fiber reinforced laminate composite is considered. This problem is treated as an interface crack between two dissimilar anisotropic materials with both a square-root stress singularity and an oscillating, square-root singularity at the crack tip. The mechanical and thermal properties of the composite plies are obtained by means of homogenization. Several interfaces are considered including 0° //90°, +45° // − 45°, 30° // − 60° and −30° //60°, as well as an interface between two woven plies of an MD laminate. The double slash represents the position of the delamination relative to the ply directions. The first term of the asymptotic expansion of the stress and displacement fields will be presented together with the interface energy release rate, phase angles and the J-integral.