Relevance. The need to predict air convective movement in mine shafts in emergency modes of mine ventilation associated with the cessation of their forced ventilation. The occurrence of extended convective vortices in the shafts intensifies heat and smoke transfer in the event of a fire, and reduces as well the amount of natural draught, which poorly ventilates the mine after the fan is turned off. Knowledge of the conditions for the occurrence of thermal convection in shafts will allow for more accurate planning of measures to combat mine fires. Aim. To develop a methodology for assessing the convective stability of air in relation to the conditions of mine shafts. Objects. Mine shafts. Methods. Analytical and numerical modeling of convection occurrence and development in the mine shaft; comparative analysis of methods for estimating the convective stability of an unevenly heated medium in the gravitational field. Results. The authors have analyzed the methods for estimating air convective stability depending on the value of the vertical temperature gradient. It is shown that analytical methods of estimation in approximations of a compressible fluid in hydrodynamics, an ideal gas in meteorology, or by the sign of a vertical density gradient give results that differ significantly quantitatively. In order to identify the most adequate method of assessment in relation to mine conditions, the authors carried out numerical simulation of the convective air movement in the shaft at different values of its vertical temperature gradient. By calculation, it was established that the still air in the shaft when heated from below turns out to be even more stable than follows from the most optimistic estimate – the critical temperature gradient of the air is almost 5 times higher than the adiabatic one. The obvious reason for the result obtained is the stabilizing effect of viscosity forces, which increases many times over in the cramped conditions of mine shafts, preventing the development of convection, which occurs in a free atmosphere with much lower convective forces. Based on the results obtained, it is concluded that the meteorological criterion for assessing the convective stability of air in relation to the conditions of mine shafts is not suitable, since it is excessively rigid. Convection occurs at a vertical temperature gradient of ~ 46 °C/km, which is possible either when cold outside air enters the shaft or when there are heat sources in the shaft that heat the air more than the heat exchange with the surrounding rock mass.