Rock mechanics and rock pressure present a very complicated problem,and one which has been little studied for the deposits in the eastern regions of the Soviet Union. At the same rime, the special features of such deposits as. for example, the u~ck Kuzbass coal seams require special multiple investigations of a complex of problems in rock mechanics and rock pressure, together with the development of suitable methods for this purpose.Experience in working the Kuzbass deposits has revealed rbat on the deeper horizons, 250-300 m from the surface. the mining operations become difficult, mainly owing to the high rock pressure. This pressure is directly or indirectly associated with the stability of workings on lower horizons, rock bursts, shock bumps, eruptions of clay into the waste, mutual interactions between workings in neighboring seams, underground fires, and gas emission. Research on these topics will largely determine the prospects for working Kuzbass deposits at depths of 500-600 m or more [1,2].Studies of rock mechanics, begun by the Siberian Branch of the Soviet Academy of Sciences in 1957, are aimed at finding the scientific basis for working mineral deposits, in particular the deep-lying0 tectonically complicated beds of the Kuzbass.The main aim of this work was the experimental and theoretical study of stresses and strains in the rock and of rock pressure phenomena near mining-out workings.Some mathematical resul~ were found by means of methods of the mechanics of a continuous medium at the institute of Mining of the Siberian Branch of the Academy of Sciences of the USSR. under the direction of L A. Kunin [3][4][5][6][7]; these results were based on ideas put forward by Barenblatt and Khristianovich [8]. In formulating this problem the authors consider a homogeneous isotropic elastic medium occupying some plane region divided by thin beds of foreign material (coal seams) with possibly quite varied mechanical (including theological) properties. The stress-strain sram of the medium is studied, and the mechanical characteristics of these is reduced to a boundary condition, in view of the fact that these beds are very thin in comparison with the characteristic dimensions of the problem, it is assumed that the boundary conditions are satisfied on certain lines or the lines of faulting (the boundary between the seam and the coumzy rocks). There may be total adhesion, frictional slip, or zero tangential force between the coal seam and the rocks. In formulating the boundary conditions it is assumed that the coal seam is elastic, and that the vertical displacement of the roof at the boundary with the seam is directly proportional to the acring szresses and the compliance of the seam h/E0, where h is the thickness of the seam and F~ the elasticity modulus of the coal In the zone near the face it is assumed that u~e coal is plastic. The method of attack allows us to introduce various combinations of boundary conditions at the line of faulting, representing parrs of the coal seam. the waste space (with or without su...