In this paper the delamination of coating subjected to compressive stress on a cylindrical substrate is considered. This problem is particularly interesting in oxide coatings on wire elements exposed to extreme temperatures and in ceramic coatings on turbine engine blades or other components that operate at high temperatures. Using the results of Hutchinson (Hutchinson, 2001, “Delamination of Compressed Films on Curved Substrates,” J. Mech. Phys. Solids, 49 , pp. 1847–1864) the aforementioned problem is discussed from the aspect of application of the linear elastic fracture mechanics (LEFM) concept for an interfacial crack. The energy release rate and mode mixity for the case of the coating delamination in the axial and radial directions are determined. It is shown that the results also depend on whether the substrate is convex or concave. Delamination in the radial direction in the case of the concave substrate is harder, but it is more likely when the substrate is convex. Delamination in the axial direction is equally likely in both cases. The results presented in this paper justify the application of the concept of linear elastic fracture mechanics for an interfacial crack for explaining the influence of the elastic characteristics of the substrate on the buckling delamination of the coating.