Under the assumption that the stress-strain state of the layer has a high degree of variability, and also under an upper bound on the vibration frequency, the author obtains approximate expressions for the contact stresses in relation to the displacements of the layer. These expressions make it possible to avoid the solution of the three-dimensional problem of elasticity for the body, and to consider the layer under the action of an additional load, which can be interpreted as taking into account the effect of elasticity of the body and of its additional masses.