A mesoscale model for fibre kinking onset and growth in a three-dimensional framework is developed and validated against experimental results obtained in-house as well as from the literature. The model formulation is based on fibre kinking theory i.e. the initially misaligned fibres rotate due to compressive loading and nonlinear shear behaviour. Furthermore, the physically-based response is computed in a novel and efficient way using finite deformation theory. The model validation starts by correlating the numerical results against compression tests of specimens with a known misalignment. The results show good agreement of stiffness and strength for two specimens with low and high misalignment. Fibre kinking growth is validated by simulating the crushing of a flat coupon with the fibres oriented to the load direction. The numerical results show very good agreement with experiments in terms of crash morphology and load response.