Edge delamination cracks in laminated composite strips are analyzed with the aid of the enriched finite element method, wherein the asymptotic singular solution for a delamination crack is incorporated into finite elements. The strip is assumed to be in the state of generalized plane deformations including extension (compression), bending or torsion. Comparison of the numerical results with those from other methods is made to confirm the solution. The crack growth stability is examined for a couple of ply orientations in terms of the energy release rate and mode mixity.