A review of theoretical representations and experimental data on rotational motions of elements of a continuous medium is given. Description of wave rotational motions is impossible in the framework of the classical theory of elasticity, but it is allowed within the scope of generalized continua models (the Cosserat microspolar model, moment and gradient models, etc.), as well as in the framework of A.V. Vikulin’s model, in which the stresses are described by a symmetric tensor. Physical, geological and geophysical data are given that confirm both rotational approaches to describing the blocks and plates composing a geomedium and the existence of rotational waves.