A review of works is presented in which new models of continuum mechanics generalizing the classical theories of elasticity are being intensively developed. These models are used to describe composite and statistically inhomogeneous media, new structural materials, as well as complexly constructed massifs in mine and ground conditions; and in the study of phenomena occurring in permafrost under the influence of thawing processes. A characteristic feature of the theory of media with a hierarchical structure is the presence of explicit or implicit scale parameters, i.e. explicit or implicit non-locality of the theory. This work focuses on the study of the non-locality effects and internal degrees of freedom reflected in internal stresses that are not described by the classical theory of elasticity, but can be potential precursors of the development of a catastrophic process in a rock mass.