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This thesis explores new territory with the theoretical investigation of the use of FSS in HPM applications. Work was performed in a simulation environment where rectangular and ring-shaped FSS elements were evaluated. Incident electric field levels of 0.5MV/m were propagated toward the FSS in a plane wave that was perpendicular to the surface. Results show that the total electric field in the apertures of the FSS can reach more than 6MV/m. This necessitates the use of high strength dielectric materials surrounding the FSS to reduce the risk of electrical breakdown. It is shown that a dielectric of only 2.5mm thick on each side of the FSS eliminates the risk of breakdown.