In this paper, a quasi-continuous analysis based on the VIB method for the tensile deformation of single-wall carbon nanotubes is presented trough taking the hyper elasticity theory as a theoretical foundation. As a result of the noncentrosymmetric atomic structure of some nanometer materials, the effects of local nonuniform deformation on the calculation of the stress and strain can be basically restrained by means of searching the relative balance positions of every atoms at different stages of deformation. The tension response of a single-wall carbon nanotube is analyzed, and their axial force-strain curves can be obtained. Furthermore, the strain and the stress at the onset of fracture of the single-wall carbon nanotubes under tension can be estimated, which are in agreement with the results of MD simulation.
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