In this article, finite element methods and molecular dynamics method were employed to simulate covalent bonds between carbon atoms in nanotubes with a linear beam element. Single-walled carbon nanotubes with different structures, and a wide diameter and longitudinal range were analyzed. The effect of geometric parameters of CNTs including diameter, length, and chirality on the Young's and shear modulus of the nanotubes was independently investigated. Also, the decrease in Young's modulus of CNTs was determined due to the presence of a vacancy defect and an increase in the number and location of the defect. The results showed in all three types of defective nanotubes (armchair, zigzag, and chiral) with a small-diameter, Young's, and shear moduli increased with incrementing the nanotube diameter. Also, in all three types of structures with a diameter greater than 20 $$\AA $$ , the effect of the diameter of the nanotube is significantly reduced, and the Young's and shear modulus approached those of a graphene sheet. For nanotubes with a diameter greater than 20 $$\AA $$ and a length greater than 240 $$\AA $$ , the effect of nanotube dimensions on Young's and shear moduli was negligible and the only factor affecting the mechanical properties of these nanotubes was the chirality or structure of the nanotube, and among the studied nanotubes, the vacancy defect had the greatest impact on Young's modulus of chiral nanotubes, with a chiral angle of 15.49 $$^\circ $$ . Also the results demonstrated that the diameter of the nanotube has a greater effect on the elastic properties than the length of the nanotube. Comparing the results obtained for armchair, zigzag, and chiral nanotubes, the vacancy defect had the greatest impact on Young's modulus of chiral nanotubes. The present theoretical study highlights the important role played by vacancy defected CNTs in determining their mechanical behaviors as reinforcements in multifunctional nanocomposites.