The problem of the stressed state of a carboniferous massif containing a coal seam worked out by a working belongs to the class of flat elastically plastic problems. To construct the stress field in the marginal extremely stressed zone of the seam, the Coulomb–Mohr criteria for the transition of the seam to the limiting state, as well as the methods of bulk medium mechanics developed by V.V. Sokolovsky, were used. If the rock layers of the soil and the roof of the coal seam are not strong enough, then the limiting state occurs first in it, and then at some distance from its edge and in the layers of rocks of the massif. It occurs when the reduced stress in the rock layers reaches the value of the reduced stress in the seam corresponding to the strength limit of the layers for uniaxial compression. After that, the seam and rock layers work together. Based on the constructed stress field of the seam, the problem of the stress state of the array is reduced to the problem of elasticity theory and solved by the method of boundary elements and successive approximations. According to the results of the computational experiment, the parameters of the reference pressure of the reservoir being worked out, depending on the width of the working, were obtained. Comparative estimates are given with similar parameters when mining a seam in the soil and roof of which there are strong layers of rocks.