The present paper is devoted to an issue of possible localization of waves propagating within a structure that consists of a film connected to a backing material by a substrate. The substrate is initially damaged. In the first approximation, the film model in the present paper is assumed to be a string on an elastic foundation with a coefficient depending on the substrate damage degree. The elastic foundation imitates the substrate and backing material effects on the film. Initiation of a string delamination resulted from the structure damaged at localized oscillations caused by impact loads has been considered. At loading, the initial damage of the substrate is changing in time and space according to the proposed law of the damage growth. It has been shown that at impact the cause of the string substrate material damage increase can be localized oscillation modes. The localized mode existence depends on the relation between initial substrate rigidity and main material rigidity. The impact energy is redistributed between propagating waves and localized waves in such a way that the latter make the main contribution to the growth of the material damage.