The main aim of this study is to develop a method for evaluating the stability of fluid movement in rigid reservoirs under coupled vertical and horizontal loads. The liquid inside the shell is assumed to be an ideal and incompressible one. For numerical simulation the method of integral equations is used. The third Green’s formula is applied, and a two-dimensional system of singular integral equations for determining the velocity potential is received. For shells of revolution, this two-dimensional system of singular integral equations is reduced to one-dimensional. After solving the spectral problem, the eigenvalues and eigenmode of own liquid vibrations are obtained. These modes are further used as basis in the study of forced fluid vibrations under harmonic loads. Fluid vibrations in the rigid cylindrical tank have been studied. Resonance phenomena are considered including parametric resonance. The Ince-Strutt diagram is used to study the zones of stability under vertical loads. Horizontal loads and combined horizontal-vertical loads are also studied. The sub-resonance frequencies of the forcing forces are studied. The effect of Rayleigh damping is considered. The developed technique can be used to tune out unwanted resonant frequencies in the design of fuel tanks.