The implementation of cohesive elements for studying the delamination process in composite laminates is presented in this paper. The commercially available finite element software ABAQUS provides the cohesive element model used in this study. Cohesive elements with traction-separation laws consist of an initial linear elastic phase, followed by a linear softening that simulates the debonding of the interface after damage initiation is inserted at the interfaces between the laminas. Simulation results from two types of composite laminate specimen, i.e., a double cantilever beam and an L-shape, show that the delamination process on laminated composites begin with debonding phenomena. These results indicate that the implementation of cohesive elements in modeling the process of delamination in laminated composite materials, using the finite element method, has been successful. Cohesive elements are able to model the phenomenon of delamination in the specimens used in this study.