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This paper attempts to investigate the application of the higher-order continuum theory in studying the size effect of single-walled carbon nanotube (SWCNT).Based the higher-order constitutive model that has been derived by the present authors, a higher-order Bernoulli-Euler beam model is established for SWCNTs, in which the size effect is involved into the higher-order elastic constants.Different to the classical beam theory, the second-order deformation gradients with respect to the axial direction are also considered.