The stability of a liquid plug inside a vertical tube depends on the balance between the weight of the liquid and the capillary forces. Contact angle hysteresis is required for a liquid plug to be at equilibrium; it has a stabilizing effect. On the other hand, capillary drainage into corners or grooves destabilizes liquid plugs and may lead to their dislocation. Following a detailed literature review about the influence of the tube cross-section on plug stability, this paper provides original numerical and experimental results obtained in tubes of circular, regular polygonal and fluted cross-sections. The cross-section may affect stability either through direct modification of the menisci curvature, or through that of apparent contact angle hysteresis. The latter was characterized experimentally for the first time to our knowledge in tubes of non-circular cross-section. Among the studied shapes, the fluted and triangular ones are the most promising for destabilizing liquid plugs. They both promote capillary drainage. Besides, fluted tubes reduce stability by a direct effect on curvature, while triangular tubes decrease apparent contact angle hysteresis. These findings could help improve the performance of two-phase closed thermosyphons of small dimensions by mitigating liquid hold-up in the condenser section. Indeed, recent advances in additive manufacturing processes enable the fabrication of thermosyphons with very complex shapes. Other devices such as fuel cells could also benefit from the optimization of their geometry to prevent channel occlusion.