Due to their exceptionally high specific strength and specific stiffness, single-and multiwalled carbon nanotubes (SWCNTs and MWCNTs) are widely used as reinforcement in metallic, ceramic and high-performance polymer matrices. The mechanical properties, including stiffness, strength and bending characteristics, of carbon nanotubes (CNTs) are greatly influenced by a number of factors, including CNT diameter, chirality, number of concentric walls in MWCNTs, chemical functionalization, surface defects and so forth. However, the challenges associated with the separation of a single CNT and its experimental characterization lead to less reliable and varying estimations of mechanical properties. This chapter presents a careful overview of the elastic and inelastic mechanical properties of isolated single-and multiwalled carbon nanotubes, determined using tedious experiments and elaborated computational methods and their dependence on nanotube physical/chemical properties.