Rock mass damage at great depths near underground openings is often of a zonal character.However,the classical elastoplastic theory fails to explain sufficiently all properties of zonal failure structures.A new non-Euclidean mathematical model for highly-stressed rock mass was developed based on the principles of mechanics of defected material and non-equilibrium thermodynamics.Methods were developed to determine model parameters that provide satisfactory correspondence between the experimental findings concerning faulted zonal structures near openings at great depths and mathematical calculations.The mechanism of this phenomenon was discovered which consisted in a periodical character of stresses in the surrounding rock mass and development of tensile macrocracks at zones of maximal tangential stresses.Main relationships between the cracking zone width and rock mass strength were established. Rock mass damage at great depths near underground openings is often of a zonal character. However, the classical elastoplastic theory fails to explain all properties of zonal failure structures. A new non-Euclidean mathematical model for highly-stressed rock mass was developed based on the principles of mechanized of defected material and non-equilibrium thermodynamics. Methods were developed to determine model parameters that provide satisfactory correspondence between the experimental records concerning faulted zonal structures near openings at great depths and mathematical calculations. mechanism of this phenomenon was discovered which consisted in a periodical character of stresses in the surrounding rock mass and development of tensile macrocracks at zones of maximal tangential stresses. Mines relationships between the cracking zone width and rock mass strength were established.