  We construct multi-field generalisations of the Cosserat continuum model on
the basis of the square lattice model that takes into account rotational degree
of freedom of microstructural elements. This approach allows us to model not
only long but also short wavelength fields of displacements and rotations. The
accuracy of the wave solutions is examined. The dispersion relations of plane
harmonic waves for multi-field Cosserat continuum models are obtained and
compared with those of the basic model.
