A penny-shaped delamination is modeled as a flat octahedral shaped crack between layers of a cross-ply laminate. The fibers of the laminate intersect the edges of the delamination at angles of 0 • /90 • , +45 • /−45 • , 90 • /0 • and −45 • /+45 • as one proceeds along the delamination edge. Two lay-ups are considered, a cross-ply consisting of two layers, and a symmetric composite, consisting of three layers. The delamination is always between two of the layers. Both tension and shear are applied to the outer boundary of the body. Stress intensity factors about the delamination edge are calculated by means of a conservative M-integral. These are employed to calculate the interface energy release rate and corresponding phase angles. Use is made of existing experimental results to predict the location of propagation along the edge of the delamination. It was found that the most dangerous regions along the delamination front occurred for the 0 • /90 • or 90 • /0 • interfaces.