The paper proposes a method of reconstruction of the Cosserat elastic moduli using the measurements of velocities of the p-wave and the high-frequency twist wave as well as the low-frequency asymptotics of a shear wave dispersion relationship. It is shown that in the case of a general isotropic Cosserat continuum, the information obtained from these wave measurements is insufficient for the complete moduli reconstruction. The reconstruction is shown to be possible in the case of a 3D isotropic Cosserat continuum governed by at most four independent parameters. Such a continuum is suggested for a particulate material consisting of spherical particles connected by normal, shear and rotational links. Another case when the full reconstruction is possible consists of 2D orthotropic Cosserat continuum modelling particulate material with square packing of cylindrical particles and 2D isotropic Cosserat continuum modelling with hexagonal packing of cylindrical particles. In the 2D materials, the measurements of p-wave velocity and the shear wave dispersion relationship are sufficient for complete reconstruction of all moduli. A phase shift method and reconstruction algorithms are presented. © 2014 Springer-Verlag Wien.