With the development of finite element (FE) codes, numerical modelling of delamination is often considered to be somewhat commonplace in modern engineering. However, the readily available modelling techniques often undermine the truthful understanding of the nature of the problem. In particular, a critical review of the representativeness of the numerical model is often diverted to merely a matter of numerical accuracy. The objective of this paper is to scrutinise the representativeness of cohesive zone modelling (CZM), which is readily available in most of the modern FE codes and is used extensively. By concentrating on obtaining the converged solution for the most basic types of delamination, a wide range of modelling complications are addressed systematically, through which complete clarity is brought to their FE modelling. The representativeness of the obtained predictions, i.e., their ability to reproduce the physical reality of the delamination process, is investigated by conducting a basic verification of the results, where the capability of the model to reproduce its input data in terms of critical energy release rates is assessed. It is revealed that even with converged solutions, input values of the critical energy release rates for the simple cases considered are not reproduced precisely, indicating that representativeness of the CZM for more general applications must not be taken for granted.