In spite of the considerable attention which has been focused on diffraction by perfectly conducting structures, little success has so far been achieved when finite conductivity is introduced. It is now shown that with the assumption of suitable boundary conditions, the problem of diffraction at a metal sheet is capable of exact solution. Corresponding to each of two fundamental polarizations, a pair of Wiener-Hopf integral equations is derived from which to determine the electric and 'magnetic' currents present in the sheet. One of these equations is subjected to a rigorous solution, and from it the solutions of the other three are deduced by symmetry considerations. Use of the generalized method of steepest descent then serves to determine the diffracted fields. The case of a circularly polarized incident wave is also briefly discussed and a comparison presented between the theoretical and experimental forms of the scattered field; good agreement is obtained.