The cylindrical antenna problem has been tackled using the spectral iteration technique. An iterative scheme is employed for improving on an initially assumed form of the current distribution. Use is made of the fast Fourier transform (FFT) algorithm, and the cumbersome process of matrix inversion is circumvented. Consequently, this method is capable of handling a larger number of unknown coefficients in the expansion of the current distribution. Furthermore, it provides a convenient means of testing for the satisfaction of the boundary conditions on the surface of the antenna. Convergence criteria for the iteration process have been established and the use of an acceleration procedure is illustrated. Different types of source models have been investigated, and the convergence of both local and nonlocal parameters is also discussed.