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[en] Application of the principle of energy balance to a rigid indenter in contact with a thin elastic layer on a flat rigid substrate provides a very simple derivation of the detachment criterion which earlier has been obtained by much more complicated asymptotic analysis. The simple criterion is additionally confirmed by the fully three-dimensional simulations of contact with a coated rigid substrate using the recently developed formulation of the boundary element method for coated media. The found detachment criterion is applied to contact of indenters of various shape. In the case of flat-ended indenters, the adhesive strength occurs to be proportional to the area of the face of the indenter (independently of the shape). The asymptotic criterion is also used for calculation of the adhesion strength of indenters having arbitrary shape and is illustrated with a case study of a contact of a rough indenter with a coated substrate.