A detailed study of a Rayleigh wave propagating on the surface of a mi
cropolar elastic circular cylinder in an azimuthal direction is consid
ered. At the cutoff frequency if the particle displacement is purely a
zimuthal and equivoluminal, then only this type of wave exists. A numb
er of deviations from the results of the classical theory are observed
. For example, the phase velocity corresponding to the same branch is
given to be single valued, whereas it seems to be multivalued at some
intervals. Due to the micropolar effect there exists an extra wave who
se frequency spectrum is also obtained. The dependence of the microrot
ation and couple stress amplitudes on depth are evaluated. The frequen
cy of the Rayleigh wave increases due to the micropolar effect.