The article provides a solution to the problem of the stress-strain state of the base in the field of karst dip. The problem is considered in the linear formulation for a layer of bounded thickness weakened by a cylindrical notch. The solution is obtained in polynomials based on the use of the Solyanik – Crass stress functions satisfying a quasi-harmonic type differential equation. The main task was solved on the basis of using the principle of superposition. The verification of the obtained solution was carried out on the basis of a comparison of the components of the stress and displacement tensor with the results of numerical solutions. Graphs constructed using the Mathcad mathematical complex and the Plaxis software complex were considered. Their analysis showed good convergence of the results.

Keywords: Karst, cylindrical cavity, stresses, displacements, isopolis, linear formulation, mixed problem