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Micro/nano-components often exhibit size effects in micro-electro-mechanical systems. A torsional vibration model of micro circular shafts is established based on nonlocal elasticity theory in this paper. Concrete examples are presented for three kinds of boundary conditions. It is shown that according to nonlocal elasticity theory the predicted natural frequencies of the torsional vibration decrease in comparison with the results based on classical continuum mechanics, and the differences are much larger with a smaller external characteristic scale (such as radius of cross section ) or for higher modal frequencies. Vibration frequencies decrease and the nonlocal scale effects disappear gradually with the increase of cross section radius. Vibration mode functions and relative rotation angles are also observed, of which the former are consistent with those predicted by classical continuum theory. Furthermore the selection of internal characteristic scale is discussed. A numerical example proves that lattice constant of material is very close to the scale mentioned, which may he approximately adopted as the internal characteristic scale in micro/nano-mechanics. [ABSTRACT FROM AUTHOR]