This paper discusses the application of metamaterials for creation of effective soundproof enclosures used in building. A brief overview of the studies of sound emission of single-layer bending-oscillating fences is provided. The main principles of the self-coordination theory of wave fields are discussed, which allows for the calculation of sound insulation of both single- and multilayer fences with finite geometric sizes. Generalized frequency characteristics of the sound reduction index (sound insulation) and limiting values of sound insulation have been found for the single-layer lightweight fencing and the multilayer lightweight enclosure (sandwich panels). The reserves of increasing of sound insulation of a fence have been studied that are defined as the difference between its limiting values of sound insulation and its sound reduction index. The methods for reducing of resonant sound transmission through single-layer lightweight fences are also discussed. Two new types of soundproof metamaterials with a periodic structure providing new wave properties of the natural oscillations field have been developed. Changing the parameters of bending waves has been experimentally confirmed to lead to a decrease in the resonant sound transmission through a lightweight enclosure and, consequently, to an increase in its sound insulation. The excess of the sound reduction index of the studied samples over the known “mass law” has been discovered. For two-layer lightweight fencing, the sound insulation has been improved without increasing the surface density or thickness. For a multilayer lightweight sandwich panel, an increase in sound insulation is achieved with a slight increase in its surface density (up to 2%) and thickness (up to 8%).