Numerical simulation of the mechanical behaviour of composite structures with stress concentrators is fraught with a number of difficulties. First of all, the assumption of linear elastic behaviour of the material in the stress concentrator zone will lead to significant inaccuracy in determining the failure load. Thus, the weight advantage of using a polymer composite decreases. Another problem is the choice of finite element size. The traditional approach based on mesh convergence testing does not take into account potentially nonlinear deformation and damage accumulation near the stress concentrator area in the composite. Furthermore, the failure load of the composite with a stress concentrator is significantly influenced by its mesostructure. The reinforcement features directly affect the accumulation of damage and non-linear deformation of the material. In this article, two constitutive models of composite for finite element calculations that take into account nonlinear deformation and damage accumulation in the composite we considered. The possibilities of the models for assessing the failure load of the composite were demonstrated on fabric-based carbon fibre-reinforced polymer (CFRP) specimens with round holes. Firstly, tensile tests on open-hole specimens with off-axis lay-ups [15°]10, [30°]10 and with symmetrical lay-ups [±15°]5, [±30°]5, [±45°]5 were performed. These lay-ups provided different levels of shear deformation in the specimens. Then, the possibility of using a constant size of finite elements for holes of various diameters was analysed. The constitutive models provide a failure load prediction error of no more than 10% for most of the considered lay-ups.