Analysing Frequency Selective Surfaces (FSS) often requires solving integral equations that may have asymmetric and singularity behaved kernels. These singularities together with the array geometry can introduce significant complexities to the solution of the problem. The thesis deals with the solution of such equations using a spectral iterative method. The analysis is based on minimising an error criterion, which is defined as the difference between the scattered and impressed waves. Computer models have been developed as a means of predicting the radiation performance of single and multiple layer FSS. The research involves two separate but related studies. The first study is concerned with finite arrays of conducting elements. The effect of the dielectric substrate and size of the arrays to the scattered field is examined. In the second study the iterative scheme is modified accordingly in order to solve a set of integral equations for a multilayer array where each layer is assumed to be of infinite extent. The analysis takes into account the interlayer coupling and the dielectric substrates/superstrates adjacent to the array elements. The results obtained from both studies are compared with the method of moments solution as well as with experimental results.