For the coal industry it is extremely important to solve the problem of accident-free operation of the end sections of longwalls and the sections of extraction drifts adjacent to them.Considerable concentration of stresses and strains in these areas is a reason for increased failure of rocks and increased movement of the contour, leading to excessive deformation and damage to drift props.Failure in the end sections of a longwall often proceeds in dynamic form (rock bursts and sudden outbursts) and it is accompanied by severe consequences, prolonged delays at the stope, and injury to workers.According to data in [i], in these areas 64% of the dangerous roof falls occur.In recent times in view of the changeover to pillar-free technoloRy, the importance of this problem increases still more, because stable retention of the lon~wall-drift junction makes it possible with the minimum losses to maintain the working beyond the longwall and to reduce the volume and rate of development of the field by 40-45%.An effective solution to these problems is Dossible On the basis of a deep knowledge of the mechanics of the phenomena occurring, based on consideration of adequate spatial models of the rock mass, which is also governed by the complexity of these studies.Calculation of the spatial stress--strain state (SSS) for the rock mass in the region of a stope cavity in general and in the junction area of an extraction drift with a longwall by accurate analytical methods is almost impossible, because it requires solution of a boundary problem for the cavity with the most complex geometry.Well-known theoretical studies in this direction are based on some idealization of actual conditions, which make it possible to obtain specific resuits to the detriment of accuracy.Here it is possible to isolate three groups of scientific work.The basis of work in the first group is the treatment of deformation of roof rock in the junction as deformation of a rock plate with different support conditions alon~ the contour (see, e.g., [2,3]).These conditions depend on the production scheme adopted in the end section of the stope (mainly on where the driving station is located, i.e., in the drift or in the longwall), and also on variants of single or double use of the drift.A method is used for evaluating an aPbitrarily supported plate [4] whose deformation proceeds along lines of an inverted "closed envelope" shade.As a result of calculations the size of the zone of roof rock separation at the junction and the maximum deflection of the plate are determined, from which prop parameters are selected (supporting capacity and pliancy). This is the main method for increasin~ the stability of junctions and achieving safe operation in these areas.The second group is represented by references [5,6] in which the SSS is considered for an elastic isotropic (transverseLy isotroDic) seam in the junction region of the drift with a longwall.It is assumed that in view of the mechanical properties of the seam and the surrounding rocks (rock stiffness is one of two o...