Large-scale molecular dynamic simulations of the axial deformations in single-walled carbon nanotubes have been performed using an O(N) tight-binding method. Our simulations indicate that under large strain, 0 K stress is remarkably sensitive to helicity, and that a zigzag nanotube and an armchair nanotube are the stiffest, respectively, under elongation and compression regimes. Furthermore, the elastic properties of a graphite sheet have been investigated using a simple harmonic potential and an analytic bond-order potential. The results suggest that the unique elastic properties of carbon nanotubes originate from those of a six-membered ring.