This chapter presents a thin-film barrier technology for flexible electronics, as well as the factors influencing the barrier's ability to stop permeable gases in air. For the purpose of cost reduction and barrier complexity, single dense inorganic barrier layers of aluminum oxide made by atomic-layer deposition (ALD) are being studied. A thin layer of an inorganic film such as SiO2, SiNx, or Al2 O3 deposited on the flexible plastic substrate can serve as a barrier layer with the required impermeability to oxygen and moisture. The barrier properties of polymeric films are described using two measured quantities: the gas permeability (P) and the vapor transmission rate (VTR). Two approaches to significantly improve the barrier performance have been explored: increasing the film density and producing multilayer structures. This chapter gives a brief introduction of the mechanics and brittle failure mechanisms of single and multilayered films on flexible substrates.