The aim of the present paper is the theoretical investigation of the mechanical properties of carbon nanostructures of graphene and single-wall carbon nanotubes by using nanoscopic and macroscopic approaches. The nanoobject structures in free and deformed states were considered and the corresponding energies were computed in the framework of quantum mechanics methods by using the original software package of semi-empirical programsNDDO/sp-spd (developed in the Institute of Applied Mechanics, Russian Academy of Sciences) in parallel computations. The nanostructural deformations were prescribed in the approximation of the mechano-chemical deformation coordinate. The deformation forces were described by the energy gradients in selected coordinates of microscopic deformations. The mechanical characteristics of nanoobjects such as Young's modulus, rigidity coefficients, works done in deformation, critical stresses, and relative elongations in fracture were calculated in the framework of the macroscopic linear theory of elasticity; the deformation forces determined by quantum mechanical calculations were used in the corresponding relations. It was found that the mechanical characteristics of single-wall carbon nanotubes (CNT) depend on their diameter and chirality, and the deformation properties of a graphene sheet are asymmetric with respect to two normal extension modes directed along the "zigzag" and "armchair" on the sheet edges. The calculated mechanical characteristics are in good agreement with the experimental data known fromthe literature, in both the values and the deformation asymmetrywith respect to different deformation modes. © 2010 Allerton Press, Inc.