Composite materials due to high strength and stiffness to their weight ratio are widely used in different structures. Hence, it is necessary to predict their failure behavior under loading. The delamination due to interlaminar stresses at free edges is one of the most important damage modes in laminated composites. In this study, this mode in cross-ply and angle-ply laminates has been investigated using a cohesive zone model. The advantage of this method is the possibility of modeling the delamination initiation and propagation without requirement to the presence of initial crack and remeshing. Hence, at first an interface element based on bilinear cohesive law was implemented in Ansys. Next, laminated plates with different lay-ups under uniaxial tension loading were modeled. Also Hashin’s failure criteria were used to predict ply damage initiation. Numerical results show that in angle-ply laminates with small fiber angle orientation, delamination in the shear mode is the dominant mode in the loss of structural strength. The numerical and experimental results for global load-displacement response show a good agreement. Also numerical results show that in cross-ply laminates even under in-plane loading, the damage behavior extremely depends on the stacking sequence. Studies show that in cross-ply laminates under uniaxial tension, if 90o plies are inserted in top and bottom surface of the laminate, the mode I delamination and matrix cracking will start later.