A generalized synthesis technique for a new class of high-order and wideband 3-D frequency selective structures (FSSs) is presented in this paper. First, a general circuit model with shunt short-ended stubs and an i-section non-uniform transmission line is discussed, whose frequency response can be synthesized with Chebyshev functions over a wide frequency range. Following the synthesis procedure, all the circuit parameters can be derived from the specifications of the filtering response, such as filtering order N (≥ 4), fractional bandwidth (FBW), and equal-ripple return loss (RL). Then, the general circuit model is applied to design high-order and wideband 3-D bandpass FSS, which is physically realized by using stacked printed circuit board pieces etched with slotlines and microstrip lines. As an example, a fourth-order 3-D FSS with FBW = 80% and equal-ripple RL = 10 dB is designed to show the establishment of good relationship between the circuit model and the physical model. To further improve the frequency selectivity, another two coupling paths independent of the main transmission path are created by simultaneously adjusting the FSS thickness and the separation of slotline sections, thus introducing two transmission zeros at both skirts of the passband. Both design examples are fabricated and measured. Good agreement between measured results and simulated ones indicates that the proposed synthesis method can provide an efficient and accurate solution to design such a class of wideband and high-order 3-D FSSs.