A new general formulation of the problem of determining the electromagnetic field resulting from a finite electric-current source located above a plane is presented. The plane surface is assumed to have electrical properties that vary in one direction only. The analytical technique used has the following properties: (1) the source or exciting field is arbitrary; (2) the resulting equations directly relate the unknown electric field intensity and the source field intensity; and (3) the boundary conditions evolve directly from the formulation as auxiliary equations. Solutions of the problem for the electric surface field are given for the following special cases: (1) a surface with one simple discontinuity; (2) a surface with two simple discontinuities; and (3) a surface with a discontinuity involving a finite region. Expressions for the electric field in all regions of the surface are given in each case, and these expressions are used to develop radar-range equations and radar cross sections for ground-wave radars.