Recent experimental investigation on FSS arrays forming waveguides (FSGs) and horns showed that incident electromagnetic energy can be guided and radiated at specific frequencies. This thesis aims to provide the theoretical understanding of the waves propagating inside a cylindrical FSS waveguide. With immediate applications on horn antennas the research deals with cylindrical guides, made entirely from double periodic arrays. The theoretical analysis begins as a standard electromagnetic boundary value problem. The formulated system of algebraic equations is solved either for the complex propagation constant, by an iterative procedure or, for the fields. The analysis makes use of the Floquet modal expansion, the current representation as a set of sub-domain basis functions and the Method of Moments. Initially, the thesis is concerned with single periodic structures, which is a special case to the analysis. The efficiency of the model to provide stable and valid results is examined. Next the elements are finite dipoles. The effects of the dipole resonance to the propagating and radiating characteristics of the FSS is closely investigated. Other aspects include the effects of the periodicity and the element size. The investigation concludes with an FSG with square loop elements. Validation of the results for some designs is made by comparison with measured data.