This paper analyzes the experience of fundamental and applied research in the field of theory and practice of dealing with sudden outbursts and other gas-dynamic phenomena (GDP). Classifications are given depending on the mining-geological and mining-technical factors that predetermine the manifestation of sudden outbursts. The gas-dynamic factor is considered as a result of the “coal–gas” system activation under external influences. Effective means and methods for preventing GDP at great depths are substantiated. A generalized structural and logical diagram of the constituent elements for taking outburst prevention measures is generated. An algorithm for conducting computational experiments is formulated. A geomechanical model developed for the rock mass surrounding the drifting face is substantiated. A comparative analysis of the mine working stress–strain state (SSS) using traditional technology for its construction and the proposed method for reducing the risk of rock outburst is conducted. The effect of drilling advanced wells is specified separately for each SSS component. The occurrence of a significant effect of de-stressing an outburst-prone rock mass is confirmed by calculations of the formation of additional outcropped surface planes. The results of computational experiments have been generalized, and a methodology has been developed for determining the rational parameters of the technology for conducting mine workings with drilling of advance.