In this study, we use molecular simulations based on the AIREBO potential function to find new results on the effective Young's modulus of single‐walled carbon nanotubes. For large tensile loadings, this effective Young's modulus is found to decrease significantly down to only 45% of its initial value, with a decrease rate which is found, here, to be nonlinear. The dependence with radius or chiral angle of this nonlinear decrease rate is studied. For all the tubes tested, we also find values of the initial Young's modulus in good agreement with those of previous studies, and a linear increase of the tubes' surface area for large axial deformations.