The integral equation for the diffraction of a plane scalar wave by a locally reacting, planar, finite scattering surface is treated, the surrounding being either a free space or a uniform locally reacting plane. The surface is described by a ’’generalized reflectivity’’—a bilinear function of the reflection factor containing two free parameters. By proper choice, the validity of Kirchhoff’s Fourier approximation of the diffraction pattern can be extended. Also the analytical treatment of some simple scattering and inverse scattering problems is alleviated. Numerical solution methods are then considered; apart from the direct method, only applicable to small equation systems, an iteration procedure is developed, based on Neumann’s successive‐approximation method. Proper choice of the two free parameters leads to fast convergence in most cases. The methods are tested with Schroeder’s quadratic‐residue‐sequence diffusors. Agreement with the measurements is acceptable but not perfect.