Axial compressive strength is a key design parameter for CFRP structures.One of its limiting factors is the non-linear shear behaviour of the unidirectional ply.We investigate the estimation of this behaviour from those of its constituents by computational homogenisation with an hexagonal unit cell and different random microstructures with smooth and clustered fibre distributions.A random microstructure without clusterings predicts the shear modulus most closely.However, the modelled shear responses converge at higher loadings so that an hexagonal model is sufficient to estimate the non-linear shear behaviour and in turn give accurate estimations of measured compressive strength