Abstract <p>A solution to the thermoelastic problem in a thin layer on a curvilinear cylindrical surface is proposed. Generality of the problem and its solution are achieved by selecting a coordinate system maximally adapted to the surface profile. The general integration of the two-dimensional Laplace thermal equation is performed with respect to a specific thermal coordinate. The system of thermoelastic equations for the layer is integrated assuming that its thickness is small compared to the surface radius of curvature. Based on the general conditions for the extremum of the von Mises criterion, material failure criteria at the outer and inner boundaries of the layer are determined. The proposed method can be used to predict the durability of thermal barrier coatings for gas turbine engine blades.</p>