An assumed hybrid-stress finite element model together with a composite multilayer element incorporating the technique of contact analysis is employed to analyze a composite laminate with delamination cracks originating from transverse cracking. Contact without friction on the crack surfaces and three-dimensional interlaminar stresses are taken into account. Once the contact zone exists, the assumed stress field satisfies the traction reciprocity conditions on the contact area acid a transformation matrix is employed to deal with the contact conditions for the displacements on the contact zone. The interlaminar stresses and stress intensity factors are calculated accurately. As examples, cross-ply composite laminates with delamination cracks originating from transverse cracking under extension are studied. The influence of ply thickness on the growth of delamination cracks is also evaluated. The comparisons between the present results and referenced solutions show the high accuracy and validity of the present technique. Copyright (C) 1996 Elsevier Science Ltd