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A technique for modeling wire objects interacting across or penetrating the planar interface which separates two half-spaces is described. The moment-method treatment is employed, based on the thin wire approximation to the electric-field integral equation, with the effect of the interface included via the Sommerfeld integrals. The computation time associated with evaluating the latter is substantially shortened by using an interpolation-based technique plus asymptotic field expressions. Although developed specifically for the wire problem, the procedure is also applicable, with slight modification, to modeling surface objects as well. Special care is taken to account for the charge discontinuity that occurs at the point a wire penetrates the interface. Example calculations are shown for a monopole antenna driven against ground stakes and simple ground screens, the fields of buried objects, and a simple electromagnetic pulse (EMP) simulator.