Complete analytical solution for the normally incident water wave scattering by a porous flexible vertical elastic plate or tensioned membrane is found. The physical problem in a half-plane is reduced to a couple of equivalent quarter-plane problems by allowing incident waves from either direction of the structure. In the same way, quarter-plane boundary value problems are posed for solid wave potentials that are solutions of the scattering problem involving a rigid structure of the same geometric configuration. Then, two novel integral relations are introduced to establish a link between the required solution wave potentials and few resolvable solid wave potentials. Explicit expressions for the scattering quantities such as the reflection and the transmission coefficients are obtained. Also, the deflection of the flexible vertical structure and the solution potentials are determined analytically. Numerical results for the explicitly derived scattering quantities and structure deflections are presented. © 2020 Elsevier Ltd