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Abstract: This work presents a numerical analysis of damage of composite materials with polymeric matrix reinforced with carbon fibres subject to static tension. Verification of numerical analyses was conducted with experimental methods – strength tests and microstructural observations. The methodologies applied were: the material damage modelling methodology based on XFEM (eXtended Finite Element Method) and contact interactions in a fibre–matrix connection layer using the CZM method (Cohesive Zone Method – Surface-based Cohesive Behaviour). ABAQUS/Standard software was the applied numerical tool. Microstructural analysis and numerical simulations indicate the fact that initiation of composite material damage takes place at the interface as a result of cracking and loss of fibre/matrix connection. This results in weakening of the composite microstructure in this area through the initiation of a reinforcement cracking process, which leads to further structural degradation, consisting in propagation of matrix cracking and, as a result, complete damage of the composite structure. The presented research of carbon/epoxy composite damage confirmed the adequacy of the prepared numerical model. [Copyright &y& Elsevier]