The authors present a method of applying fast Fourier transform (FFT) techniques to the solution of the electric field integral equation (EFIE) on finite periodic bodies using the methodof- moments (MoM). These techniques are used to speed matrix–vector multiplications in an iterative solution of the discretized EFIE, and to save memory space required for storing the impedance matrix. An individual array element can have arbitrary three-dimensional structure and be electrically connected to its neighbors. The method is independent of the type of basis functions used, of the method of surface patching, and of the field excitation (which need not be periodic). The algorithm can be applied both to scattering and to antenna problems. The authors demonstrate improvements in speed-of-execution and memory required.