This article uses the asymptotic homogenization method to investigate the mechanical characteristics of single-walled carbon nanotubes. The asymptotic homogenization method has been used to derive the equations for the homogenized elastic properties matrix. Then, MATLAB is used to model nanotubes and implement the finite element simulation. Two types of chiralities, including armchair and zigzag, are taken into account in this regard. Young's modulus and shear modulus have been estimated for both armchair and zigzag nanotubes in accordance with the relationships between the derived coefficients and molecular mechanical characteristics. Investigations have been done into how diameter and orientation affect the mechanical characteristics of carbon nanotubes. The research's findings are corroborated and generally consistent with those found in other articles.