A systematic design method for high-order dualband bandpass frequency selective surfaces (FSSs) with a low profile is derived from classical filter theory and presented here. To complement the design procedure, a multilayer double-slot resonator unit cell topology is proposed for realizing dual-band operations. For simplicity, the resonators are made to work for only a single polarization. To design the FSS, first, a classical dual-band bandpass filter circuit is designed by performing successive frequency transformations on a lowpass prototype. The filter is then transformed into a form resembling the equivalent circuit of the proposed multilayer FSS structure. Finally, the transformed filter is mapped to a set of FSS geometrical parameters. The method presents very few inherent limitations to realizing a diverse range of filter responses. The resulting designs lend themselves to fabrication since very few layers of metallization are required. Two FSSs with third-order passbands at 4 and 7 GHz but different passband characteristics are designed and verified numerically. One of the designs is fabricated and experimentally verified. The overall thickness of the designs is 0.08λ _l where λ _l is the free-space wavelength at 4 GHz. The unit cell size is approximately λ _l /8.