In the absence of significant mass forces, the behavior of liquid fuel under microgravity conditions is determined by surface tension forces, which are intermolecular forces at the interface of two phases. The paper posed and solved the problem of equilibrium and small oscillations of an ideal liquid under microgravity conditions, and also quantified the influence of various parameters: the contact angle α0, the Bond number, the ratio of the radii of the inner and outer walls of the vessel and the depth of the liquid. For the coaxial-cylindrical vessels, there were obtained expressions in the form of a Bessel series for the potential of the fluid velocities and the free surface displacement field. The study relies on the analytical and experimental data available in the literature and proves the reliability of the developed numerical algorithm. Findings of research show that for and r, with the physical state of the wetted surface being unchanged, the shape of the free surface tends to be flat and the contact angle has little effect on the intrinsic vibration frequency of the free surface of the liquid. The results obtained can be used to solve problems of determining the hydrodynamic characteristics of the movement of liquid fuel in outer space.