In this study, a three-dimensional finite element (FE) model for armchair, zigzag and chiral single-walled carbon nanotubes (SWCNTs) is proposed. To create the FE models, nodes are placed at the locations of carbon atoms and the bonds between them are modeled using three-dimensional elastic beam elements. The FE model is used to investigate the influence of chirality and Stone-Wales defects on the ultimate strength (Ultimate stress and ultimate strain) of SWCNTs. Results indicate that Stone-Wales defect significantly reduces the ultimate stress and strain of armchair CNTs. But this defect has a negligible effect on the ultimate strength of zigzag nanotubes. Based on the results, the crack growth path in zigzag and armchair nanotubes have 90 and 45 degree angle to the long axis of the nanotube, respectively.