Cu/PET composite films are widely used in a variety of wearable electronics. Lifetime of the electronics is determined by adhesion between the Cu film and the PET substrate. The formation of an anisotropic nanostructure on the PET surface by surface modification can enhance Cu/PET interfacial adhesion. The shape and size of the anisotropic nanostructures of the PET surface can be controlled by varying the surface modification conditions. In this work, the effect of Cu/PET interface nanostructures on the failure mechanism of a Cu/PET flexible composite film is studied. From observation of the morphologies of the anisotropic nanostructures on plasma-treated PET surfaces, and cross-sections and surfaces of the fractured specimens, the Cu/PET interface area and nanostructure width are analyzed and the failure mechanism of the Cu/PET film is investigated. It is found that the failure mechanism of the Cu/PET flexible composite film depends on the shape and size of the plasmatreated PET surface nanostructures. Cu/PET interface nanostructures with maximal peel strength exhibit multiple craze-crack propagation behavior, while smaller or larger interface nanostructures exhibit single-path craze-crack propagation behavior.