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This paper investigates the size effects in the dynamic torsional response of single-walled carbon nanotubes (SWCNTs) by developing a modified nonlocal continuum shell model. The purpose is to facilitate the design of devices based on CNT torsion by providing a simple, accurate, and efficient continuum model that can predict the frequency of torsional vibrations and the propagation speed of torsional waves. To this end, dispersion relations of torsional waves are obtained from the proposed nonlocal model and compared to classical models. It is seen that the classical and nonlocal models predict nondispersive and dispersive behavior, respectively. Molecular dynamics simulations of torsional vibrations of (6, 6) and (10, 10) SWCNTs are also performed, the results of which are compared with the classical and nonlocal models and used to extract consistent values of the nonlocal elasticity constant. The superiority and accuracy of the nonlocal elasticity model in predicting the size-dependent dynamic torsional response of SWCNTs are demonstrated.