We consider the problem of distributing the stress-strain state (SSS) characteristics in the body arbitrarily loaded on the outer surface and weakened by a physical cut with a thickness of δ₀. It is assumed that δ₀ parameter is the smallest possible size permitting the use of the hypothesis of continuity. The continuation of the physical cut divides the body into two parts interacting with one another by means of a contact with δ-layer. Due to constant average stresses and strains over the layer thickness, the problem reduces to the system of variational equations for the displacement fields in the adjacent bodies. The geometry of the bodies under consideration has no singular points and, as a consequence, has no singularity of stresses. The use of average characteristics makes it possible to disregard a form of the physical cut end. The obtained solution can be used for processing of experimental data in order to establish the continuity scale δ₀. The entered structure parameter for silicate glass is assessed using known mechanical characteristics.