The micromechanics of kink band formation in open-hole fibre composites under compressive loading is described. The objective being the development of a methodology for designing of structural components with open-holes. Our results explain why failure by kink band formation propagates from the edges of an open-hole in a direction almost perpendicular to the loading direction and why the 0 degree plies govern the compressive failure of an open-hole laminate. The proposed design methodology accounts for the microstructure, including the fibre/matrix bonding, and the nonlinear behaviour of the constituents, enabling it to prevent local failure at the hole edges, or global failure, by kink banding of a laminate containing stress concentrations.