Purpose. Development of a semiempirical method to identify rock pressure on the support of underground mine roadways as well as substantiation of its efficient use area taking into consideration the depth of the mine roadway, its geometry, and hardness of enclosing rocks. Methodology. Theoretical studies on geomechanical processes taking place in the neighbourhood of roadways using analytical mathematical methods as well as numerical ones. Analysis of the research results and their generalization are involved. Findings. Methods to identify load (i.e. rock pressure) on the supporting structures have been developed. The methods are based upon the proposed calculation technique for the rock stability coefficient at the boundary of contact between a collapsing arch of the rock (i.e. fall arch) and undisturbed rock mass, i.e. at the boundary of elastic share of peripheral rock mass, and non-elastic one. A stability coefficient has been proposed in the form of projection on vertical axis of forces holding the rock mass, limited by a fall arch, to projection of shear forces. Originality. For the first time, an analytical and empirical method to identify natural arch over horizontal and vertical mine roadways has been proposed involving their depth, geometry, parameters of rock strength, and its gravity. The abovementioned is the key distinction of the proposed method from the known semiempirical technique by M.M. Protodyakonov to determine natural arch as well as support load. Practical value. The findings make it possible to predict stability of horizontal mine roadways using mathematical methods. In this context, the depth, geometry, and hardness of enclosing rocks are taken into consideration.