This paper presents the self-stabilisation features of a hopping gait during underwater legged locomotion. We used a bio-inspired fundamental model of this gait, the underwater spring-loaded inverted pendulum model, to numerically derive quantitative (dimension of the basin of attraction, Floquet multipliers, mean horizontal speed) and qualitative (shape of the basin) features which characterise the self-stability of the system. Furthermore, we compared the results obtained with a terrestrial self-stable running model (i.e. the spring-loaded inverted pendulum with swing-leg retraction) to highlight the role of water-related components in relation to dynamic legged locomotion. The analysis revealed fundamental morphological and actuation parameters that could be used to design self-stabilising underwater hopping machines, as well as elucidating their role with respect to stability and speed. Underwater hopping is a simple and reliable locomotion, as it does not require complex control feedback to reject significant disturbances. Thanks to its high self-stabilising property, underwater hopping appears to be a reliable alternative locomotion for underwater robots.