The problem of stresses and displacements of an oblique-layered massif near a mine working, which is located entirely in one of the rock layers, is considered when the mine is tested by the effects of cleaning works in a coal seam. This effect is taken into account by specifying a system of normal and shear forces at the boundary of the lower layered half-plane with a hole. The problem is solved by imposing the complex Kolosov – Muehehelishvili potentials and Fourier integral transforms. Based on the method of Fourier integral transforms in the theory of elasticity, a system of integral with respect to normal and tangential contact forces is obtained for the case of two different layered half-surfaces. In this work, systems of integral equations are obtained in solving the problem of the reference pressure on an obliquely buried coal seam near the mine working. In this paper, the method of integral Fourier transforms in the theory of elasticity, obtained a system of integral with respect to normal and tangential contact forces for the case of two different layered half-surfaces.