We consider wave propagation in soils and rocks modeled as an isotropic linear elastic reduced Cosserat continuum to take into account the proper rotational dynamics of heterogeneities contained in media. In such a medium, translations and rotations are kinematically independent, the stress tensor is nonsymmetric, and the couple stresses are zero. We consider plane wave propagation, construct the Green’s function for the harmonic point source in the 3D unbounded medium, and study the Rayleigh-type wave. The compression wave for the isotropic case is the same as in the classical medium. The shear wave is coupled with rotation and differs both from the classical case and from the case of the full Cosserat continuum. There are forbidden bands of frequencies where some waves do not propagate, localization phenomena are possible, and strongly dispersive behavior is observed near these bands. For the Rayleigh wave, there is also a cutoff wavenumber for one of the dispersion branches.