The phenomenon of wave localization in hydroelastic systems leads to the strength concentration of radiation fields. The linear method considers the process of localization to be the formation of nonpropagation waves (trapped modes phenomenon). The presence of such waves in the total wave packet points to the existence of mixed natural spectrum of differential operators describing the behaviour of hydroelastic systems. The problem of liquid and oscillating structure interaction caused by the trapped modes phenomenon has been solved (membranes, dies). The interaction of the liquid and elastic structures with inclusions can lead to localized mode formation. In the case of solitary wave motion in nonlinear elastic media, contacting with the liquid, these solitons can be interpreted as `moving inclusions'. The analytical solution for solitary waves has been found. If the soliton speed v₀ is more than the velocity of sound c₀ in the liquid, the solitary waves strongly slow down. If c₀ is close to v₀, then a resonance can be observed and solitons move without any resistance. If the soliton speed is less than c₀, the solitary wave slow-down is negligible, compared to the case v₀>c₀.