<p>In the Cosserat micropolar theory, the stress tensor is asymmetric, with the antisymmetric part representing micro rotations, for example, of material particles such as grains in granular porous media. The solution of the differential equations includes the classical P and S waves, as well as two micro-rotation waves, whose effects become significant at high frequencies. Explicit expressions for the phase and group velocities as functions of frequency and wavenumber for a plane wave are derived. In homogeneous media, the P wave is not affected by the micro-rotations, and the S wave is coupled to the micro-rotation waves, it is dispersive and has the same velocity as in the classical theory of elasticity at low frequencies. To our knowledge, there are no simulations of micro-rotation waves as single wavefronts in the literature; only their effects on the particle displacements are simulated. A direct grid method, based on the Fourier pseudospectral method for computing spatial derivatives and a fourth-order Runge–Kutta algorithm for time integration, calculates the wavefield in the space-time domain and simulates micro-rotation wavefronts. A stability analysis verifies the conditions under which the algorithm solves the Cosserat differential equations.</p>