Carbon nanotubes (CNTs) are rolled form of graphene sheet with unique properties due to the covalent bonds between carbon atoms. In this research, different structures of CNTs are studied for a wide range of diameter and length to determine the influence of chiral angle on their shear and bending modulus. Covalent bands between carbon atoms are simulated using linear beam elements based on molecular mechanics and finite element method. By using finite element analysis, the effects of diameter, length and chiral angel of nanotubes on mechanical properties under torsional and bending loading conditions are studied. The results show that zigzag CNT has the least shear and bending modulus comparing the armchair and chiral structures. Chiral nanotubes with angles smaller than 17 degrees has less shear modulus comparing armchair ones. But, for larger angles, chiral nanotubes has the largest shear modulus. Also, bending modulus of chiral CNTs is larger than armchair and zigzag structures.