A method for the numerical modelling of mechanical behaviour of nanocomposite materials, which is based on computational homogenization as a multiscale method, is presented in this work. As an introduction, a brief history of the nanomaterials and theoretical background about the carbon nanotubes and numerical modelling of the carbon nanotubes is presented. Also, the theory about composite materials is given, since it is also the basis of the nanocomposite materials theory. A special attention is devoted to the nanocomposite matrix and reinforcement interaction. A method of numerical modelling of those interactions, which are mainly based on the weak van der Waals forces, is presented. An algorithm is developed for analysis of those interactions, which enables modelling of bonds between nanocomposite matrix and nanotubes or between two different layers of multiwalled carbon nanotubes, based on input parameters. Since the problem of modeling nanocomposite structures is a multiscale problem, one part of this work is dedicated to multiscale modeling methods, especially to the first order computational homogenization. Computational homogenization and representative volume element are the basis of the presented software for numerical modelling of the nanocomposites. For the purpose of the software verification, 4 models of the nanocomposite material, with different characteristics, are presented. Obtained results are compared with the results from the other authors.