The design of coatings is like designing a system. Every coating has one or more specific functions that determine the choice of materials, and its architecture. In the case of environmental barrier coatings the topcoat must be chemically inert to the atmosphere. In high-temperature applications the stresses arising from thermal expansion mismatch between the topcoat and the substrate must be ameliorated. In this article we consider the design of an intermediate layer of a multilayer coating system with the explicit objective of managing thermal expansion difference between the topcoat and the substrate. The design is based upon a columnar architecture where the columns serve as flexible beams to accommodate relative displacement without fracture. The value of the maximum stresses in the beam and in the topcoat are calculated and used to develop a map with fail and safe regimes. The safe region is defined by the prevention of fracture in the beams, since their fracture would precipitate delamination of the topcoat. As a rule of thumb the topcoat thickness should be less than the width of the columns for safe operation (this condition changes somewhat with the aspect ratio of the columns). A larger aspect ratio of the columns also promotes safe design. We further consider how the tractions induced by the thermal stresses on the surface of the substrate may influence the intrinsic fracture strength of the substrate. The stresses in the coating are predicted to have an insignificant effect on the intrinsic fracture strength of the substrate.