The diffraction of a plane small amplitude sound wave incident upon a semi‐infinite thin elastic plate is investigated theoretically. The problem is formulated in terms of an integral equation relating the discontinuity in pressure across the diffracting plate to its flexural displacement and the usual fourth order thin plate differential equation governing the flexural motion of the plate when driven by the pressure discontinuity. This pair of coupled equations is then shown to be amenable to solution by the Wiener‐Hopf method. A perturbation procedure, valid in the limit of increasing plate stiffness, is employed to obtain expressions for the sound fields radiated by and transmitted through the plate as well as for the diffracted sound field.