We present relations for the calculation of equivalent stresses in a coating. Plots of equivalent stresses against the difference in Poisson's ratio between the substrate and the coating have been constructed. It has been shown that the calculated curves give a good fit to the magnitudes of the maximum normal and equivalent stresses for different coatings. Analysis of the results obtained shows that it is necessary to take into account the effect of Poisson's ratio of the coating on the equivalent stresses and, accordingly, on the limiting stressed state of the coating in the strength analysis of coated structural elements and in the experimental determination of cohesive strength in laboratory tests. When designing coated structural elements, one should seek the combination of the elastic properties of the substrate and coating at which the magnitude of the equivalent stresses in the coating achieves its minimum value.