The paper considers nanocomposites, reinforced with aligned carbon nanotubes (A-CNTs). Nominally aligned, the CNTs in the forest are wavy, which has important consequences in downgraded mechanical properties, and influences electric and thermal performance. The most detailed geometrical model of A-CNTs was proposed by Stein and Wardle (Nanotechnology, 27:035701, 2015). It creates a centerline trajectory of a CNT in steps, each step defining a section of the CNT, growing in the alignment direction with certain deviations. The paper, starting from this framework, formulates a model of the CNT geometry, which is based on the concept of correlation length of the CNT waviness and maximum admissible CNT curvature and torsion. The value of the maximum curvature can be linked to the buckling criteria for CNTs, or derived from ab initio and finite element modelling. It is used as a limiting factor for the growth, defining the waviness and tortuosity of the CNTs. The CNTs in the forest are placed in a random non-regular way, using Voronoi tessellation. The full paper includes investigation of the proposed algorithm for several values of the CNT volume fraction (in the range 0.5%…8%), the dependency of the modelled geometry on the curvature, and the apparent twist of the CNT centerlines. The modelling results are compared with experimental observations in 3D TEM imaging.