A group of polygonal carbon nanotubes (P-CNTs) have been designed and their mechanical behavior was investigated by classical molecular dynamics simulations. The research aimed at exploring the effects of structure, temperature, and strain rate on the mechanical properties. The results indicate that the Young's modulus of P-CNTs is lower than those of circumcircle carbon nanotubes (C-CNT). Moreover, with an increase in the number of sides to the polygons, the Young's modulus increases and is much closer to that of C-CNT. The effects of temperature and strain rate on the mechanical properties of P-CNTs show that the higher temperature and slower strain rate result in a lower critical strain and weaker tensile strength. In addition, it was found that the critical strains of P-CNTs are dependent on the tube size. Finally, we used the transition-state theory model to predict the critical strain of P-CNTs at given experimental conditions. It is expected that this work could provide feasible means to manipulate the mechanical properties of novel P-CNTs and facilitate the mechanical application of nanostructures as potential electronic devices.