Molecular dynamics (MD) simulations were used to investigate the elastic properties of carbon nanotubes (CNTs). Displacements were loaded to CNTs on the tension deformation simulations. In order to better understand the relationship between Young’s modulus and the structure of the CNTs, different chiralities and diameters were involved. It is found that the Young’s modulus will be no more sensitive as in the single-walled carbon nanotubes (SWCNTs) with increasing walls. The tension deformation results also indicate that SWCNTs have better elastic property compared to multi-walled carbon nanotubes (MWCNTs).