Abstract The article presents the process of modeling delamination of a woven composite material by the finite element method. The models contain a detailed mesostructure in the form of weave geometry. The delamination occurs in the DCB (Double Cantilever Beam) test with the critical energy release rate as a propagation criterion. The methods used, especially Virtual Crack Closure Techniques (VCCT), have allowed us to present the delamination front changes during the propagation. To further investigate the influence of the mesostructure, additional fully homogenous models were analyzed. Load-displacement graphs, typical for DCB tests, are presented. The obtained results show how the presence of detailed geometry of the composite influences the development of damage.