Abstarct: In the present thesis, firstly the buckling and vibrational behavior of defective single-walled carbon nanotubes under axial, tortional and bending loads has been investigated using the ABAQUS software. Further, the influence of various vacancy and stone-wales defects on the critical buckling load, related displacement, tortional and bending moment and related angle has been studied. Then, after proposing a new model by adding van der Waals force, identical analyses have been preformed for the perfect and defective double-walled carbon nanotubes. In this section, the buckling behavior of DWCNTs under axial, tortional and bending loadings and the effect of van der Waals force, number and position of defects on these CNTs were obtained. The nessecity of getting special experimental conditions and also time consimung of atomic simulations were the major motivation for proposing this new structural mechanics model, which contains the proper accuracy and short runtime, and it does not have the limitations of previous methods. Actually, the present model is a combination of other structural models which can remove the most of their errors. In order to model the axial and tortional intractions, the nonlinear connectors and for angle variation and van der Waals intractions, the nonlinear springs were used. Then, the obtained results were compared to the continuum model results and it can be shown that the buckling behavior of CNTs have many similarities to the buckling behavior of cylindrical shells (with a wall thickness of 0.066 nm and Young’s modulus of 5.5 TPa). Finally, the results of the present model were compared to some of the reliable molecular, structural and continuum models. It can be concluded that the present model has high accuracy and low time and also it has capabilities that the existing structural models do not have.