<p>Within the framework of the 3D linearized theory of stability of deformable bodies for the case of a 2-D problem, the problem of compression of a semi-bounded body (base) with a coating layer along a crack located on a rectilinear interface of different media sliding without friction against each other was investigated. An analytical-numerical approach was proposed that allows reducing the original boundary-value problem formulated in terms of potential harmonic functions to an eigenvalue problem for the Fredholm integral equation of the first kind, which was studied numerically using the Bubnov–Galerkin method. In this case, the specified integral equation was obtained in a general form for a wide class of combinations of two hyperelastic materials, for the potential of which the case of equal roots of the characteristic equation was realized, and the specification of the models of body materials occurs only at the final stage of solving the problem. For compressible materials with a harmonic potential and incompressible materials with the Bartenev–Khazanovich potential, the critical values of the loading parameters in the problem were determined, their dependence on geometric, and physical-mechanical parameters were investigated, and a comparison of the obtained results with the results of a similar problem on the compression of a piecewise homogeneous half-plane with rigidly connected components along an interface crack was carried out.</p>