By utilizing the fourth-, sixth-, eighth-, and tenth-order elastic moduli tensors of graphene a highly nonlinear constitutive model for it is proposed. Subsequently, an accurate analytical formulation, describing the entire tensile behavior of single-walled carbon nanotubes (SWCNTs) from their initial unloaded states through their ideal strengths, is made possible. The angle of twist which is a critical parameter that varies with the tensile loading is also calculated within the current framework. The estimated value of the theoretical strength of SWCNTs with different chiralities and radii as well as that of graphene ranges from 0.39 to 0.44 TPa. Some peculiarities associated with chirality of 15° are observed.