An approximate asymptotic high-frequency result which is convenient for engineering applications is obtained for the field exterior to a smooth perfectly conducting convex cylinder when it is illuminated by a plane wave. This result is uniform in the sense that it remains valid within the transition regions adjacent to the shadow boundaries where the pure ray optical solution based on the geometrical theory of diffraction (GTD) fails, and it automatically reduces to the GTD solution exterior to the transition regions where the latter solution becomes valid. Furthermore, this result is expressed in the simple format of the GTD, and it employs the same ray paths as in the GTD solution. This uniform result is not valid in the close neighborhood of the cylinder; hence a separate asymptotic result is presented for this special case in a form which is also convenient for applications. The asymptotic results presented here are useful for predicting the patterns of antennas radiating in the presence of convex conducting cylindrical structures.