In this paper torsional deformation of the carbon nanotubes is simulated by molecular dynamics method. The Brenner potential is used to set up the simulation system. Simulation results show that the carbon nanotubes can bear larger torsional deformation, for the armchair type (10,10) single wall carbon nanotubes, with a yielding phenomenon taking place when the torsional angle is up to 63°(1.1rad). The influence of carbon nanotube helicity in torsional deformation is very small. The shear modulus of single wall carbon nanotubes should be several hundred GPa, not 1 GPa as others reports.