In the present paper, a boundary value problem associated with scattering or radiation of water waves involving a vertical barrier present in deep water is reduced to dual integral equations. Noting that one of the integrals of the dual integral equations is bounded at both ends of the interval complementary to the one in which it is defined, it is found that a solution of the dual integral equations exists if and only if a certain solvability criterion is satisfied. Exploiting this solvability condition, the amplitude of the waves at infinity associated with scattering and radiation of water waves involving a vertical barrier have been evaluated. © WILEY-VCH Verlag Berlin GmbH.