The use of carbon nanotubes to improve the mechanical properties of polymers is one of the promising directions in materials science. The addition of single-walled carbon nanotubes (SWCNT) to a polymer results in significant improvement of mechanical, electrical, optical, and structural properties. However, the addition of SWCNTs does not always improve the polymer properties. Also, when a certain content of SWCNTs is exceeded, the mechanical properties of the nanocomposite are getting worse. This article reports the results of computer simulations for predicting the mechanical properties of polymer/single-walled carbon nanotube nanocomposites. The efficiency of reinforcing polymer composites is considered depending on the concentration of carbon nanotubes in the polymer matrix, their size and structure. The elastic moduli of the nanocomposites were predicted using computer simulations for unit cell tension (0.1%). General trends in the mechanical properties of composites with polypropylene, poly (ethyl methacrylate), polystyrene matrices and SWCNTs are shown.