A material model to predict kink-band formation and growth under a 3D stress state is proposed. 3D kinking theory is used in combination with a physically based constitutive law of the material in the kink-band, accounting for friction on the microcracks of the damaged material. In contrast to existing models, the same constitutive formulation is used for fibre kinking and for the longitudinal shear and transverse responses, thereby simplifying the material identification process. The full collapse response as well as a crush stress can be predicted. The model is compared with an analytical model, a micromechanical finite element analysis and crushing tests. In all cases the present model predicts well the different stages of kink-band formation and crushing.