A large amount of underground cavities nowadays exists throughout the Apulian region (south-eastern Italy) as a result of mining processes of soft calcarenite, which frequently followed the “room and pillar” technique. In these cave systems, pillars and septa are critical structures, whose failure can lead to a significant increment of the sinkhole hazard. The behaviour of these rocky structures in the dynamic field is poorly studied in literature, and the present study aims to investigate their dynamic stability, according to regional seismicity data. For this purpose, ideal pillar geometries were considered, for which the evolution of the stress–strain field under dynamic inputs was observed in both 2D and 3- configurations by means of parametrical finite element analysis. For shallow cavities, slender septa were found to be the most affected by the influence of seismic loading. For deep cavities, dynamic instability is observed only for rather squat septa, with the cavity width also influencing the dynamic behaviour. To quantitatively assess the septum stability, a stability index was also proposed in 2D models. Moreover, three-dimensional analyses showed a stabilizing effect in the pillar exerted by the stress component perpendicular to the earthquake.