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An analysis is presented for determining the current induced by a known transverse electric excitation on a perfectly conducting cylinder located near the planar interface separating two semi-infinite, homogeneous half-spaces of different electromagnetic properties. The conducting cylinder of general cross section is of infinite extent and the excitation is transverse electric to the cylinder axis. Two types of integral equations, the magnetic field integral equation and the electric field integral equation, are formulated, and the Green's functions for the integral equations are derived in an appendix. Numerical solution methods for solving the integral and integrodifferential equations are presented. For a strip parallel or perpendicular to the interface, a circular cylinder, and a rectangular cylinder, data are presented and discussed for selected parameters, including the case of a cylinder resting on the interface.