Carbon nanotubes (CNTs) have become a highly researched topic since their discovery in 1991, mainly due to their excellent mechanical and electrical properties. CNTs have a projected Youngâ€™s modulus of 1 TPa, high strain elastic responses and very high aspect ratios. These properties suggest that CNTs could be nearly ideal fibrous reinforcement for composite materials. Other possible applications proposed have been nano-wires, nano-scale fluid piping and nanostructures. In the present study, molecular mechanics, an empirical form of atomistic simulations, has been used to study the mechanical responses of single-walled and multi-walled nanotubes (SWNT & MWNT). These molecular simulations mimic traditional macro-scale material tests such as tension, torsion and contraction. Two molecular mechanics potentials were used in the simulations and their nonlinear behaviors analyzed. Linear isotropic continuum models were also developed whose responses match those of the simulations. These simple continuum models were verified versus bending and buckling simulations by both simple Euler beam and finite element models. The models were found to yield accurate critical buckling loads and mode shapes as compared to models presented in the literature.