Substrate materials for flexible devices are multi-layer composite structures. On top of a base polymer functional inorganic layers such as permeation barriers and conductive layers are applied. Due to the thermal mismatch between polymer and inorganic layer, the layer is compressive loaded at ambient conditions. A characteristic failure mode, occurring with compressive loaded thin layers, is buckling failure. The interface between adjacent layers fails locally, and the thin top layer bends outwards. The buckles have a characteristic width and height. These sizes are used to analyse the compressive strain, present in the layer before failure, and the adhesion quality of the failed interface. A buckle map is introduced to guide this analysis.