The deformation of single-walled carbon nanotubes (SWCNTs) under large axial strain is studied by a geometrical mapping method. The interactions between atoms in carbon nanotubes (CNTs) are described by Tersoff-Brenner potential. Results show the strain energy depends on chirality but hardly on tubes’ radii. For graphitic sheet under large axial deformation, the elastic moduli decrease with the increase of engineering strain under tension. The modulus reaches the peak value as the axial engineering strain reaches -0.08 for armchair pattern and -0.15 for zigzag pattern under compression.