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An accurate and efficient numerical solution is developed for predicting high-frequency radiation patterns of antennas mounted on curved surfaces. This solution employs the uniform geometrical theory of diffraction (UTD) and has mainly been used to analyze airborne antenna patterns. In this case the aircraft is modeled in its most basic form so that the solution is applicable to general-type aircraft. The fuselage is modeled as a perfectly conducting composite ellipsoid, whereas, the wings, stabilizers, nose, fuel tanks, and engines, etc. are simulated by perfectly conducting fiat plates. The composite-ellipsoid fuselage model is necessary to simulate successfully the wide variety of real world fuselage shapes. Since the antenna is mounted on the fuselage, it has a dominant effect on the resulting radiation pattern, so it must be simulated accurately, especially near the antenna. Various radiation patterns are calculated for military aircraft, private aircraft, and the space shuttle orbiter. The application of this solution to practical airborne antenna problems illustrates its versatility and design capability. The solution accuracy is verified by the comparisons between calculated and measured data.