In modern constructions, thin-layer coats are often used as protecting or strengthening elements. Deformations of such constructions may cause significant stresses on the interface between the base and the coat because of the difference in their physical-mechanical properties, which leads to the destruction or delamination of the cover. Of special interest is strength analysis under dynamical or vibrational impacts because of the possibility of localizing oscillations in a neighborhood of the initial inhomogeneities (such as inclusions, defects, construction elements, etc.). In this paper, on the example of the delamination of a string from an elastic substrate, the possibility of localizing oscillations on a delamination defect is demonstrated and the effect of this localization on the growth of the delamination zone is analyzed. A simplified setting of the problem is considered. The possibility of localizing oscillations on a delamination defect is demonstrated and an approximate analytical solution is constructed, which takes into account only the first symmetric form of oscillations describing the development of the initial delamination. A numerical modeling of the problem is performed, and the results of modeling are compared with the approximate analytical solution.