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We present a comprehensive synthesis procedure for designing low-profile, band-pass frequency selective surfaces composed of non-resonant constituting elements. The proposed FSSs use arrays of sub-wavelength periodic structures with non-resonant constituting unit cells with unit cell dimensions and periodicities in the range of , where is the free space wavelength. The main advantages of this type of FSS, compared to traditional ones, are that they allow for the design of low-profile and ultra-thin FSSs that can provide sharp frequency selectivity and stable frequency responses as functions of angle and polarization of incidence of the EM wave. An order FSS designed using this technique typically has an electrical thickness in the order of which is significantly smaller than the overall thickness of a traditionally designed order FSS . The proposed synthesis procedure is validated for two FSS prototypes having third- and fourth-order band-pass responses. Principles of operation, detailed synthesis procedure, measurement results of a fabricated prototype, and implementation guidelines for this type of FSS are presented and discussed in this paper.