We continue in this paper the work on the modelisation of rocks and soils in terms of the elastic reduced Cosserat continuum. The basic idea of the model is to take into account the mictrostructure of rocks and soils which influences the wave propagation, for some frequency range trapping the energy of the propagating wave by their proper rotational motion. We consider the Rayleigh wave for the isotropic case, using analytical and numerical methods. Instead of a straight line in the classical medium, we obtain two dispersion curves. The polarization differs both from the case of classical medium and the case of Cosserat continuum with couple stresses. We observe for some frequency range a strong frequency dependence. There is a forbidden band of frequencies, lying below the analogous forbidden band for an unbounded medium. It indicates the possibility of localization phenomena. For the upper branch of dispersion relation, there is also a forbidden domain of wave numbers: long waves may propagate only with one frequency. Far from the domain of frequencies where the microstructure influences the wave propagation, the medium behaves analogously to the classical one.


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