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In this work in terms of the ideas of the zone of inelastic deformations generated around stress concentrators in heterogeneous rock mass as a quasi-plastic block medium having a microstructure, rigorous criteria of rock mass stability are obtained that naturally take into account mining-geological and geomechanical conditions. Theoretical ideas added to the problems of underground structure stability permitted to provide an explanation for paradoxical, in the view of classical representations, numerous cases of m...