Article, by way of discussion, provides a description of a technique to determine the core of foundation modelfor the subsequent generation of forces and deformations in the foundation plate on a pliable base by an analytical method. The technique described in the article can also be used to determine the contact model of the base that is closest to these soil conditions, as well as to check the soil conditions for identity from the point of view of soil models. Main goal of conducted research is to obtain relationship between displacements and contact soil stresses, which is an integral Fredholm equation of the 1st kind with the core of soil model described by B.G. Korenev.