This paper reports methods to compute the equilibrium stances of a new snake-like robot designed to stabilize its head on a free water surface. To adjust rapidly the stability of the robot, this bio-inspired robot can rotate independently each body-shell, and modify the level of immersion of each module. To predict the stable stance accessible by this additional degree of freedom, a model is developed to compute the equilibrium configurations of the robot from a given parametrization of the body shape. Then, an algorithm is introduced to compute a sequence of controlled body deformations, such that the head configuration relatively to the water surface remains unchanged. Finally, we explore in simulation stances and quasistatic gaits, and investigate to what extent the buoyancy and the body deformations can be used to stabilize the head of the snake-like robot.