In recent years, new models of continuum mechanics have been intensively developed, generalizing the classical theory of elasticity. These models are used to describe composite and statistically inhomogeneous media, new structural materials, as well as for complex built rock mass in mine conditions. The paper describes the algorithm of acoustic waves propagation when active monitoring the elastic layered block media with inclusions of the hierarchical type of L-rank. Correlations for internal stresses and strains for each hierarchical rank are derived, which constitute the nonlocal theory of elasticity. The essential differences between the nonlocal theory of elasticity and the classical one and connection between them have been investigated. A characteristic feature of the theory of media with a representative structure is the presence of scaled parameters in explicit or implicit form, i.e. explicit or implicit nonlocality of the theory. In this work, special attention is paid to the study of the effects of nonlocality and internal degrees of freedom reflecting 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 massif.