Finite-difference and numerically analytical methods for solving dynamic and elastic-plastic problems of geomechanics are proposed. Using the finite difference method and on the basis of the principles of the mathematical modeling of physical processes the tensor components, which characterize the dynamic stress field in rocks around the vaulted excavation of the type under the oblique action of the stress wave on it, were determined. An iterative process, which allows calculating the components of the stress tensor and the velocity of the plastic flow of rocks around mine workings at great depths, is designed with the help of numerical analytical method. Reliability and validity of the method is confirmed by comparing the obtained calculations with the results of solutions found by other authors and experimental data.
