The cohesive element (CE) has been widely used to model delamination in laminated composites. The penalty stiffness, interfacial strength and fracture toughness are three CE parameters that often determine the accuracy of the numerical analysis by finite elements (FEs). The fracture toughness may be experimentally determined through standard fracture tests. The interfacial strength is difficult to obtain experimentally but also plays a crucial role in predictive numerical modelling. The penalty stiffness is a numerical parameter whose range of values may influence computational results. Recently, the CE has been deployed to model the initiation and propagation of delamination in composite structures where no pre-existing cracks or delamination has been assumed. The parameters are often calibrated, but comprehensive studies on the influence of CE parameters and their selection criteria remain limited in the literature. In the present paper, the effects of CE parameters on delamination modelling are systematically examined. The sensitivity of the overall progressive damage process and failure load to the assumed CE strengths and stiffness is studied based on selected examples of fracture and coupon-level tests. With varying CE strengths employed in the FE analyses, two distinct kinds of failure behaviour, namely the strength-sensitive and strength-insensitive delamination processes, have been observed, depending on the geometry and ply layups of composite materials. On the other hand, the penalty stiffness of CE mainly affects the computational efficiency and accuracy of delamination modelling. The failure mechanisms and physics behind are investigated to get better understanding on the numerical effects of CE parameters, and thus provide the selection guidelines in practical analyses.@en