The selective transmission of oblique supersonic waves through a solid plate immersed in water is studied theoretically and experimentally over a frequency range from 1.0 to 3.0 megacycles. Three cases are considered: (1) transmission for angles of incidence less than the critical angles for both dilatational and shear waves; (2) transmission for angles of incidence between the two critical angles; (3) transmission for angles greater than both critical angles. In the frequency region studied good agreement is found between the measured transmission, using the torsion disk method, and the theoretical values. Particular interest attaches to case (3). Study is also made of the supersonic transmission through a stratified medium consisting of a set of solid plates immersed in water. The acoustical Bragg law is investigated and verified experimentally.