This paper studies the sequence of fibre kinking, the fibre lock-up and the subsequent constitutive behaviour. The conditions governing these phenomena are discussed with focus on the conditions for fibre lock-up. Lower bounds for the fibre lock-up angle a and the kink band angle b are derived purely from geometrical conditions for 3D arrays of fibres, with the aim to define the termination of fibre kinking in homogenized material models for FE analysis. It is concluded that the limit of the lock-up angle is 90° for low fibre volume fractions, decreases to about 50° for fibre volume fractions common in high performance composites, and reaches zero for fully packed fibres.