  A simple macroscopic continuum elasticity theory (CET) is used to calculate
the structure relaxation of single-wall carbon nanotube (SWNT), an analytic
formula is obtained. We also expand an atomic scale three-parameter empirical
model [ T. Lenosky {\emph et al.} Nature 355, 333(1992)] in order to correctly
describe the bond-length change effects. The structure relaxation of SWNT
expected by the model is good in agreement with our CET results, and very well
consistent with the previous calculation from a first principles local density
function approximation. Using the expanded Lenosky model, we calculate the
strain energy of bending tube. The obtained results are good in agreement with
the previous theoretical expectation. It shows the model may be a good simple
replacement of some more sophisticated methods on determining carbon networks
deformations.
