Quantum/molecular mechanics and continuum mechanics have been highly developed to describe materials properties at small and large length scales. As we enter the era of nanotechnology, it has become increasingly important to model phenomena at mesoscopic length scales. Two alternative approaches, namely the "Bottom Up"approach based on quantum/molecular mechanics and the "Top Down" approach based on continuum mechanics, are frequently used to model mechanical properties and behaviors of nanotubes.Although quantum/molecular mechanics-based calculations give accurate predictions for the mechanical properties of carbon nanotubes, they are comparably complex and computational demanding. For instance, a rigorous first principle molecular dynamics can only handle a system not more than several hundreds of atoms.A continuum mechanics model, which usually provides close-form solutions, might be difficult to take into account of the effects of discrete nature of nanostructures.This study represents an effort to establish analytic methods of molecular mechanics and a set of examples that can be solved explicitly. The elastic properties and mechanical behaviors of carbon nanotubes are studied via a molecular mechanics approach. In contrast to the previous studies in which the molecular mechanics approach are only used as a numerical method, the present study gives analytic solutions to the elastic properties and mechanical behaviors of carbon nanotubes. We show that the analytic solutions are in reasonable agreement with the existing results.