A non-linear finite element analysis of compression of unidirectional carbon fibre-epoxy with fibre waviness has been carried out. Beam elements were used to model the fibres, and plane stress elements were used to represent the transverse and shear properties of the composite. Non-linear shear stress-strain response, fibre bending stiffness, large deflections, and the rotation of the material axes due to both shear strain and rigid body rotation were included in the analysis.The results show that for waviness with long wavelengths the stress at onset of shear instability is controlled by the maximum fibre misalignment angle. The maximum compressive stress reduces significantly with increasing angle. At short wavelengths the maximum stress increases due to the additional support provided by the bending stiffness of the fibres. The effect of variable amplitude waviness was also investigated and found to depend on the distance over which the variation occurs. For gradual variation, the maximum compressive stress is largely controlled by the maximum misalignment angle; for rapid variation, it is more influenced by the average angle.