Underground cut-and-cover structures are commonly designed as rigid box sections; however, in practical applications, connections between walls and slabs are frequently rather hinged (because of ease of construction). The abovementioned rigid configurations are highly sensitive to seismic ground motions, due to their important lateral stiffness and internal hyperstaticity; conversely, structures with articulated (or sliding) members have a smaller lateral stiffness, and would be significantly less affected by seismic waves, as would simply accommodate the imposed strains. This flexible solution has been widely considered in practice, but has received little attention from the academic community; this paper tries to close this gap by investigating preliminarily the seismic performance of box-section underground structures with hinged or sliding members. The well-known Daikai Station, damaged by the 1995 Kobe earthquake is analyzed in this paper as a highly relevant case study. An alternative solution is proposed for that station; both simplified and precise calculations have been performed. The simplified calculations are linear static analyses of the station-soil system; the soil-structure interaction is represented by a simple classical model. The precise calculations are nonlinear time-history analyses of an integrated finite element model of the station and the surrounding soil. Both types of analyses refer to the traditional and the proposed solutions of the station. The results of the static and dynamic analyses are satisfactorily compared; they prove that the proposed flexible solution is fully feasible and provides better seismic performance. Finally, another paper by the same authors presented a supplementary case study on a 2-story 3-bay subway station; the outcomes of these two studies could contribute to ground this constructive solution for shallow underground rectangular cut-and-cover structures in seismic areas (both for new construction and retrofit). Noticeably, this approach can be utilized for both cast-in-place and precast structures.