  The strain energies in straight and bent single-walled carbon nanotubes
(SWNTs) are calculated by taking account of the total energy of all the
occupied band electrons. The obtained results are in good agreement with
previous theoretical studies and experimental observations. The Young's modulus
and the effective wall thickness of SWNT are obtained from the bending strain
energies of SWNTs with various cross-sectional radii. The repulsion potential
between ions contributes the main part of the Young's modulus of SWNT.
  The wall thickness of SWNT comes completely from the overlap of electronic
orbits, and is approximately of the extension of
  $\pi$ orbit of carbon atom. Both the Young's modulus and the wall thickness
are independent of the radius and the helicity of SWNT, and insensitive to the
fitting parameters.
  The results show that continuum elasticity theory can serve well to describe
the mechanical properties of SWNTs.
