In this present paper, an FE approach has been presented for the elastic bending and buckling behaviors of single-walled carbon nanotubes (SWCNTs). Finite element simulations are carried out to investigate the bending deformations and buckling behaviors of SWCNTs under various conditions. Both axial compression and bending loading conditions are considered. The computed results for SWCNTs agree well with atomistic simulations in the literature and the FE approach is confirmed successfully. In this paper, the steady state structural analysis has been performed to know the strength of the CNTs using shell93 element. For analysis of SWCNT has been considered as cantilever beam and loaded at the free end. SWCNTs with different lengths, different thicknesses under various materials and loadings have been studied. In static analysis, the defections and stress induced are estimated due to axial and bending loads. Under buckling analysis, the buckling factors and corresponding mode shapes are plotted. The displacement response is plotted and reported.