Frequency selective surfaces (FSS) and other periodic gratings are often analyzed under the assumption that they are infinite in extent. Most existing methods for analyzing periodic structures are based on the use of a Floquet-type representation of the fields in a unit cell whose dimensions are typically comparable to the wavelength. In this work, a finite, truncated, version of an infinite periodic structure is dealt with directly, without the benefit of the assumption that the structure is periodic. This, in turn, requires the handling of a large number of unknowns and makes it difficult to solve the problem using conventional matrix methods. Two different iteration approaches to solving the finite FSS problem are discussed in the paper both of which employ the spectral domain formulation. The first of these employs the spectral iteration technique and the second one uses the conjugate gradient (CG) iteration algorithm. Convergence characteristics of both of these methods are investigated and the results are reported.