  A solution to the problem of water-wave scattering by a semi-infinite
submerged thin elastic plate, which is either porous or non-porous, is
presented using the Wiener-Hopf technique. The derivation of the Wiener-Hopf
equation is rather different from that which is used traditionally in
water-waves problems, and it leads to the required equations directly. It is
also shown how the solution can be computed straightforwardly using Cauchy-type
integrals, which avoids the need to find the roots of the highly non-trivial
dispersion equations. We illustrate the method with some numerical
computations, focusing on the evolution of an incident wave pulse which
illustrates the existence of two transmitted waves in the submerged plate
system. The effect of the porosity is studied, and it is shown to influence the
shorter-wavelength pulse much more strongly than the longer-wavelength pulse.
