The presence of derivatives of high order in generalized impedance boundary conditions (GIBCs) makes possible the simulation of point defects or point conductors placed on a surface. In case of the second-order GIBC, the model of a point conductor is formulated via appropriate contact condition. For a plane boundary the problem of diffraction by a point defect is accurately solvable. A scattering diagram for an arbitrary point conductor is computed. The resulting formula depends on relative Wiener capacity, which is an integral characteristic of a two-dimensional scatterer. The problem of diffraction by a periodic set of point conductors on a plane surface is solved in a closed form. ¿ American Geophysical Union 1995