When carbon nanotubes (CNTs) are grown on carbon fibres, with the goal to increase toughness of a carbon fibre reinforced composite, the compressibility of the carbon fibre bundle or a fabric decreases significantly. The pressure, necessary to achieve the desired fibre volume fraction in a composite, should be increased by several bars. The paper proposes modelling approaches for calculation of the change of compression resistance of the CNT-grafted fibre bundle and fabric. The models use a previously developed algorithm for calculation of the compression resistance of a random assembly of CNTs. Two possible scenarios for the CNT-growth positioning are considered: a CNT assembly that homogeneously fills the free space between the fibres and a CNT assembly that is localised on the surface of the fibres. The model is validated against measurements of the compression resistance of carbon fibre bundles and fabrics with CNTs grown using the CVD method. (C) 2011 Elsevier Ltd. All rights reserved.