The study investigated the impact of post-failure properties of the rock mass on the stress-deformation state in the vicinity of the underground excavation and the pressure exerted on the support. An analytical solution to the problem is presented, including the creation of inelastic zones in the vicinity of the excavation: ideal-plastic zone with residual strength and plastic zone with mild decrease of rock medium strength and taking into account the dilatancy. The analysis of the dependencies obtained was carried out using geotechnical parameters characterizing the Carboniferous rock mass of a hard coal mine. The influence of the plastic zone was determined with a mild decrease in strength to the state of stress, deformation and pressure on the rock mass support. The results of the considerations were compared with the solution, which omitted the softening of the rock mass and the solution based on the model of the elastic-plastic-brittle medium. The results of the analysis broaden the knowledge about the behavior of the rock medium in the vicinity of the excavation. The obtained solution can be further developed in order to enable its practical application, especially in conditions in which the behavior of the rock medium in the vicinity of the excavation well reflects the elastic-plastic model with a gentle drop in the strength of the rock material.