A sound barrier and method of sound insulation are disclosed. In one aspect of the disclosure, a sound barrier comprises a first, solid medium, such as a viscoelastic solid and a second medium, such as air. At least one of the two media forms a periodic array disposed in the other medium. The solid medium has a speed of propagation of longitudinal sound wave and a speed of propagation of transverse sound wave, the speed of propagation of longitudinal sound wave being at least about 30 times the speed of propagation of transverse sound wave.