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A formulation, based on the method of moments (MM), is presented for active and passive wire radiators attached to, or near, a broad class of bodies and surfaces, including open or closed cylinders of arbitrary cross section as well as finite flat or curved panels. The development expands the utility of the MM theory for various antenna problems. The analysis incorporates a special junction basis set for the antenna attachment points. Total domain and piecewise continuous expansion functions are used on the surfaces. The formulation is primarily intended for prediction of radiation patterns of wire antennas (such as monopoles and loops) on asymmetric bodies of translation, open or closed (capped). The present method has shown satisfactory agreement with published data in the prediction of antenna input impedances as well.