Purpose is to determine dependences of velocities of elastic waves in isotropic rocks and anisotropic waves with orthotropic and trans-verse-isotropic symmetry upon pressure and depth to develop evaluation criteria and control rock mass characteristics and conditions in the neighbourhood of mine workings. Methods. Continuous anisotropic medium is under consideration. Group one of boundary conditions is represented by continuity of stresses, acting normally towards the boundary while transiting from layer 1 to layer 2. Group two of the boundary conditions is as follows: displacements in the process of the boundary transition are measured continuously too. The conditions are necessary to solve a Navier Stokes equation of dynamic balance of absolutely elastic medium. The experiments were carried out with the help of geoacoustic method in terms of the acoustic parameter of compressional velocity. Findings. It has been determined that compressional velocity values, anisotropy of compressional velocity, and elastic behaviour reflect regularly structural features being pressure-dependent ones. It has been demonstrated that dependence upon the stress state, anisotropy appearance/disappearance emergence takes place or a sign inversion. Qualitative dependences have been obtained to define elastic behaviour (Е, μ, G) of anisotropic formation with orthotropic and transverse-isotropic symmetry. The dependences have been obtained through compressional velocity to consider accurately the anisotropy of the rock mass while evaluating its stress state. The research results will help estimate nature of the stress distribution; identify stress concentration zones; and zones of the disturbed rock in the neighbourhood of a mine working. That will be done using acoustic parameter of compressional velocity using a method of geoacoustic control developed by the authors. Originality. In terms of the new obtained dependences, elastic behaviour of rocks (Е, μ, G) as well as acoustic parameters of compressional velocity has been determined scientifically. They are important to design and schedule mining operations. Practical implications. Being quite accurate to satisfy the demands of practical use, the obtained research results may be applied to identify digital values of elastic behaviour (Е, μ, G); to use the method of geoacoustic control of rock mass characteristics and conditions in the neighbourhood of mine workings; and to mine deposits with complex structural and mechanical properties.