Due to their remarkable properties, carbon nanotubes have been used in many engineering applications in the form of composite. In some cases, however defects may occur and lead to poor strength of the composite. In this chapter, a finite element method has been developed to evaluate mechanical behavior of defective CNTs and graphene sheets. Stone-Wales defect (5-7-7-5) and vacancies in SWCNTs and graphene sheets with different hilarities were studied under axial load. The results show that CNTs and grapheme structures are sensitive to vacancies. However, the armchair grapheme structures have significant resistance to defect under tensile load. Present results are in good agreement with available literature. © Springer International Publishing Switzerland 2014.