Oyster® is a surface-piercing flap-type device designed to harvest wave energy in the nearshore environment. Established mathematical theories of wave energy conversion, such as 3D point-absorber and 2D terminator theory, are inadequate to accurately describe the behaviour of Oyster, historically resulting in distorted conclusions regarding the potential of such a concept to harness the power of ocean waves. Accurately reproducing the dynamics of Oyster requires the introduction of a new reference mathematical model, the “flap-type absorber”. A flap-type absorber is a large thin device which extracts energy by pitching about a horizontal axis parallel to the ocean bottom. This paper unravels the mathematics of Oyster as a flap-type absorber. The main goals of this work are to provide a simple–yet accurate–physical interpretation of the laws governing the mechanism of wave power absorption by Oyster and to emphasise why some other, more established, mathematical theories cannot be expected to accurately describe its behaviour.