The problem of scattering from infinite frequency selective surfaces (FSS) have been studied for many years by using the Floquet theorem that reduces the computation domain to a single cell (metallic patch element). These methods are already well known. A few studies have been carried out on finite surfaces, but to our knowledge, none of them have considered a general case of application. We describe two methods to compute finite FSS. For small FSS, we have used a rigorous element-by-element approach: the spectral-Galerkin method. The exact interactions between elements are taken into account. For larger surfaces, this method is no more adaptable. The computation time and the memory requirement become too large. So, we used another approach based on plane wave spectral decomposition. It allows us to consider the finite problem as a periodic infinite one. (5 pages)