An open-ended iterative technique is presented for solving a Fredholm integral equation of the second kind having a singular kernel, using a digital computer. To ascertain the accuracy of the solution, the original equation is recast analytically into a Fredholm integral equation of the first kind. The unknown function is then obtained by expanding it into a series of orthogonal functions and determining the unknown coefficients by inverting the infinite matrix (truncated at the desired order) using machine methods. The numerical results obtained from the two procedures are in complete agreement. This implies that a definitive solution of the integral equation is obtained.The problem chosen for solution in this paper arises in connection with the determination of the current distribution along a perfectly conducting open-ended cylindrical tube that is sufficiently thin so that the phase change of the plane wave exciting electromagnetic field across its diameter may be neglected. A solution for the current that converges is obtained because the structure is driven by the field along its entire length-not at some discrete point by a slice generator, as is the case in the usual theoretical model of the linear transmitting antenna. Curves for the current distribution along the structure for parallel incidence of the electric field are given. Also, the radar cross sections of several tubes for the same field orientation are determined.