We performed a numerical study to evaluate the influence of carbon nanotubes (CNTs) on the stress build-up in and around a broken fibre in a single carbon fibre/epoxy composite loaded longitudinally. The CNTs were located in the interface region and mimicked one of the two deposition techniques: 1) direct growth on the fibre or 2) dispersion in the fibre sizing. These techniques are known to produce different alignment, orientation and concentration of CNTs in a composite, which affect stress redistribution upon the fibre failure. The study was performed using a two-scale finite element model based on the embedded regions technique. The most significant effect on the stress build-up was found for CNTs aligned in the fibre direction. In this case, the crack opening displacement and the ineffective length were reduced by 15% and 28%, respectively, thus making the stress recovery in the broken fibre faster. In addition, the shear stress at the fibre-matrix interface decreased by a factor of two. These results indicate that hybridization of microscopic fibres with nanotubes aligned in the fibre direction is a promising strategy to influence the process of fibre fragmentation in a composite. [GRAPHICS]