Soon after the discovery of carbon nanotubes, it was realized that the theoretically predicted mechanical properties of these interesting structures could make them ideal for a wealth of technological applications. A number of computer simulation methods applied to their modeling, has led over the past decade to an improved but by no means complete understanding of the mechanics of carbon nanotubes. Tersoff potential has been widely used but it has since been modified many times. The latest is the second-generation reactive empirical bond order potential by Brenner and co workers, which is being used in this work for manipulating these tiny structures. We outline the computational approaches that have been taken. The elastic moduli of armchair, zigzag and chiral nanotubes have been computed. We generate the coordinates of carbon nanotubes of different chirality’s and size. Each and every structure thus generated is allowed to relax till we obtain minima of energy. We then apply the requisite compressions, elongations and twists to the structures and compute the elastic moduli. Young’s modulus is found to be dependent on tube radius for thinner tubes and attains a constant value of the order 1TPa. Our results of Poisson’s ratio and shear modulus are also encouraging and compare well with other theoretical and experimental work.