Carbon nanotubes have caught tremendous attention of the researchers during the last decade due to their excellent mechanical, electrical, optical and thermal prop- erties. The exploitation of these fibers as reinforcing agents in making strong fiber composites has been a primary research topic in the recent investigations on composite materials. Although the theoretical results are rather opti- mistic, the goal of achieving high strength of the carbon nanotube composites is still not satisfactorily realized. We report here a comparative study of the mechanical properties of single-walled, multi-walled and bundle of single-walled carbon nanotubes. Their mechanical behavior is investigated by molecular dynamics simulation, considering Brenner's second generation reactive empirical bond order interatomic potential between the carbon atoms making a tube. For a long range interaction, we have defined a weak van der Waals force which acts between different layers of a multi-walled tube or between different tubes of a bundle. Samples of three isolated armchair single-wall carbon nanotubes of different diameters, a multi-wall armchair carbon nanotube and finally a bundle of three armchair single-walled nanotubes of same diameter are taken. Their fracture pattern and buckling behavior are modeled and compared. Significant changes are observed in the mechanical properties of the samples of different types of carbon nanotubes which arise due to the interaction between the shells of a multi-walled tube or the tubes in a bundle.