Last years it has been shown that not only the hardness (H) and elastic modulus (E), but also the plasticity index (H/E) is an important parameter that characterizes the mechanical properties of composite structures (CSs). Plasticity index can serve as an indicator of the transition from elastic deformation to plastic one and to destruction [1-3]. In this paper the Cu/MgO and Cu/Si CSs were selected for the investigation of the plasticity index behavior. The nano-microhardness of the MgO and Si single crystals using as a substrate is 10-12 times higher in comparison with the polycrystalline Cu, so the CSs obtained are of type "soft-to-hard". The Cu films with thickness t=85; 470 and 1000 nm were deposited on the MgO and Si substrates by the magnetron sputtering method. Hardness (H) and Young’ modulus (E) were studied by the dynamic indentation method using the Nanotester-PMT3-NI–02 device equipped with a Berkovich indenter in a load range of Pmax=(5900) mN.             a        b Fig. 1. The dependence of the H/E plasticity index on the load, P, of CSs: a) Cu/MgO and b) Cu/Si: 1– Cu polycrystal; 2 – MgO and Si monocrystals: 3 – Cu/substrate, tCu-85nm; 4 – Cu/substrate, tCu – 470nm; 5 – Cu/substrate, tCu – 1000nm   The lowest values of the H/E parameter were revealed on the polycrystalline Cu (curve 1). The H/E(P) dependences of the Cu/MgO and Cu/Si composite structures demonstrate a more nonmonotonic shape of curves than for Cu. At low loads (5<P<100mN), the curves 3-5 (Fig. 1 a and b) suffer an abrupt decrease accompanied by oscillations, then they show a certain increase with following saturation. However, the curves of Cu/MgO and Cu/Si CSs are situated between the Cu (1) and MgO (2) curves (Fig. 1 a, curves 1 and 2) and Cu (1) and Si (2) ones (Fig. 1 b, curves 1 and 2). As follows from the above, composite structures of the "soft-to-hard" type represent new materials with higher values of plasticity index compared with properties of the film and are inferior to the substrate H/E values.