This paper presents a three dimensional finite element model for armchair, zigzag and chiral single-walled carbon nanotubes (SWCNTs). The influences of diameter, chirality and length on the elastic moduli (Young’s modulus and shear modulus) of SWCNTs are investigated. The formulation presented is based on the assumption of viewing the construction of SWCNTs as a geometric frame-like structure. The interatomic interactions of bond length, bond angle, bond torsion and non-bonded interactions are equivalent to corresponding structure features straightforwardly. The models of SWCNTs are developed according to the atomistic structure network of nanotubes. The interatomic interactions of C- C atoms are simulated via appropriate straight spring and torsional spring elements. The computational results indicate that both diameter and chirality have a significant effect on the Young’s and shear moduli of SWCNTs, while the elastic moduli are not very sensitive to the variation of length. It is also shown that with a similar radius, armchair SWCNT has a slight higher value of Young’s modulus than zigzag and chiral SWCNTs. While zigzag SWCNT has a slight higher value of shear modulus than armchair and chiral SWCNTs.