This communication presents a methodology to construct the aperture-coupled dual-mode patch resonators (AC-DMPRs)-based periodic element to realize single- and dual-band high-order bandpass frequency selective surfaces (FSSs). Initially, a single patch resonator (PR) loaded with two sets of shorting pins is theoretically studied by using the characteristic mode analysis (CMA) method and by applying periodic boundary conditions, respectively. The results demonstrate that the radiation pattern and resonant frequency of TM00 mode in the PR can be effectively reshaped and controlled by the shorting pins, so that the TM00 and TM01 modes can be simultaneously excited under the normal incidence of a plane wave. As such, the single-mode PR is transformed into a DMPR. Moreover, such DMPRs are arranged in a back-to-back manner with coupling apertures etched on the common middle metallic layer to form an AC-DMPR-based bandpass FSS element. By reasonably reallocating the resonant frequencies of these two resonant modes and etching different apertures to provide magnetic and/or electric couplings in the AC-DMPR, single- and dual-band high-order bandpass FSSs can be conveniently and flexibly constructed, respectively. Finally, the conceptual designs are validated by measurements.