In this paper, interface element with de-cohesive constitutive law is used to predict the delamination progress of laminates in which delamination is the prominent failure mode. For this purpose, a finite element program is developed to perform nonlinear damage analysis. The analyses are carried out based on the interlaminar constitutive law of elastic-plastic-damage proposed before in the literature. Delamination initiation and propagation of several laminates with dominant interlaminar shear stresses at free edges are investigated to find the failure load. It is shown that the difference between the predicted failure loads using the present study and the experimental results are 3.1% to 19.4% for various laminates.