The assessment of the reliability of a mining and technological scheme, taking into account the stress state of mine workings, depends on a combination of mining and geological, technical and technological factors. The article demonstrates the creation of a model of a rock mass and a scheme for calculating the stress state based on modern methods of mechanics of a deformable solid body.The object of study is a single mine working of great length, passed through the rock parallel to the strike of the coal seam (field drift) and located in the zone of influence of the support pressure. Due to the fact that the field drift is laid in the soil of the formation, which is a layered stratum in the zone of influence of clearing operations, the predominant load is the bearing pressure on the formation. The areas of application of the methods of complex potentials of integral equations and their combinations in solving applied problems are determined. The data of mine (field) measurements and observations, laboratory experiments and their generalizations are taken into account both when setting tasks and assigning boundary conditions, and when checking the results obtained. The mixed problem of the theory of elasticity about the contact stress on half-strips with varying along the longitudinal axis was solved; moving away from the ends, deformative properties, when these half-strips are clamped with friction between the layered half-planes.