"The ability to control the propagation of elastic waves is an issue of fundamental importance in different sectors of Structural Engineering ranging from the problem to attenuate vibrations and radiated noise, or to control localization phenomena that may induce failure mechanisms in turbo machinery and in turbines, up to the possibility to protect Civil Engineering Structures from earthquakes.The project deals with fundamental issues of control of elastic wave propagation in structured media. Such waves are dispersive, and the structured media are anisotropic, in general. The proposed approach will enable us to combine asymptotic analysis of fields and frequencies, corresponding to standing waves within the elementary cell of the structure, with accurate numerical simulations delivering the information about the dispersion properties and stop bands for Bloch-Floquet waves. The special attention is paid to structures referred to as metamaterials. In our case, the examples include an invisibility cloak for elastic waves, a shear polarizer, and filtering and focussing devices incorporating structured interfaces (flat lenses). Also, the effect of negative refraction in structured media, which is well studied for electromagnetic waves, remains a challenging problem in elasticity."