This study adopts the Tersoff–Brenner interaction potential function in a series of molecular dynamic (MD) simulations which investigate the mechanical properties under tensile loading of (10,0) zigzag, (8,3) chiral and (6,6) armchair single-walled carbon nanotubes (SWCNTs) of similar radii. The Young's modulus values of the (10,0), (8,3) and (6,6) nanotubes are determined to be approximately 0.92, 0.95, and 1.03 TPa, respectively. Of these nanotubes, the results reveal that the (6,6) nanotube possesses the best tensile strength and toughness properties under tension. Although it is noted that under small tensions, the mechanical properties such as Young's modulus are essentially insensitive to helicity, under larger plastic deformations, they may be influenced by helicity effects. Finally, the simulations demonstrate that the values of the majority of the considered mechanical properties decrease with increasing temperature and increasing vacancy percentage.