In this paper, the approaches to the study of mathematical models of the theory of linear elasticity are developed. The general formulation of the 3-dimensional problem based on the representation of the fundamental solution in the form of V. P.
Aim. Analysis of the current state of solving the problem the estimating of earth deformation fields based on continuum mechanics, improving traditional methods the estimating of horizontal deformations, definition an alternative approach and justification of ways and the algorithm of solving the problem based on it. Methodology and results. The analysis showed some shortcomings of traditional solving of the problem. In order to minimize their impact the improved method of mathematical and cartographic modeling of linear deformations is proposed.