Complete analytical solutions are obtained here for normally incident water wave scattering by vertical porous barriers of various configurations. By allowing incident waves from either direction separately, two quarter-plane problems are posed for porous potentials associated with the physical problem as well as for solid potentials associated with the scattering problem that involves the vertical solid barrier of same configuration. Then, two integral relations are introduced to establish a link between the porous and the solid wave potentials. They involve auxiliary wave potentials that describe radiation of bi-directional waves by the solid barrier. Moreover, they aid to decompose the original problem into four analytically solvable problems in a quarter-plane and to determine the porous potentials explicitly. © 2016 Elsevier B.V.