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A new approximate method for computing the current distribution on reflector antennas is presented. It employs the modified Kirchhoff approximation and leads to a vector integral equation of the second kind for the current distribution. The integral in this integral equation can be interpreted as a current due to the curvature of the reflector surface. The method is applied to a cylindrical parabolic and a cylindrical corner reflector antenna. The integral equation is solved numerically, and the computed current distributions and directive gains are compared with those obtained by solving the exact integral equation as well as with the results that follow from the application of the physical-optics approximation.