Due to high strength and stiffness in comparison with their weights, laminated composite materials are widely used in many structures such as aerospace and naval structures. Therefore, the understanding of their failure mechanisms to predict their mechanical response is of high importance. One of the major aforementioned mechanisms is the delamination which commonly occurs in skin/stiffener joints. In the present paper, a comparative study on the delamination in composite skin/stringer structures under 3 point and 4 point bending loads is performed by the finite element method (FEM) employing the cohesive elements. The detailed effects of stacking sequence on the damage of structure are investigated. A user defined interface element has been implemented in the Ansys software in continuum damage mechanics framework based on the bilinear cohesive zone model. The advantage of this method is the modeling of delamination growth without any requirements to the presence of initial crack and remeshing. Comparison of the obtained results from FEM with that of experiment justifies the capability of the employed model to predict the delamination initiation and propagation. The results indicate that in the 3 point bending load, the damage initiates from the adhesive between skin and stringer, while in 4 point bending load it initiates from the interface elements between skin layers near the adhesive bond. Finally, in order to increase the strength of skin/stringer structures, the results strongly recommends preventing the use of 45 and 90 degrees plies near each other around the adhesive bond.