The stability of comparatively more slender decks of under-deck cable-stayed bridges is studied, by considering both the critical loads and the post-buckling behaviour. A potential energy approach is applied to a simplified discrete link and spring model that allows for an exact nonlinear formulation of the equilibrium equations. The physical response is found to be dependent on the ratio of the axial stiffness of the cable-staying system to the flexural stiffness of the deck. The influence of several parameters is analysed and unstable mode interaction is observed to occur under certain geometric conditions. The presented analytical model is compared with a nonlinear finite element model that shows good correlation. Finally, some design criteria and recommendations are suggested, which are relevant for designers of this innovative typology of cable-stayed bridges.