The paper presents solutions to problems of fluid motion in partially filled cylindrical reservoirs on rolling bearings bounded by high-order surfaces of revolution. Systems of equations of motion of a reservoir partially filled with fluid on rolling bearings with straightened surfaces are obtained, and the values ​​of hydrodynamic coefficients are found for the case of a cavity in the form of a circular cylinder. Formulas are given for determining the hydrodynamic forces and moments of interaction of fluid with the walls of cylindrical reservoirs on rolling vibration mounts under horizontal kinematic disturbance. Resonance modes of oscillatory motion of a reservoir with fluid on rolling bearings with straightened surfaces are investigated. It is established that at a frequency of oscillations of a reservoir with fluid on rolling bearings bounded by high-order surfaces of revolution, much less than the natural frequency, the fluid will move together with the vessel as a single whole. The resonance phenomenon here should be understood not as an unlimited increase in the magnitude of the amplitude of the oscillations of the liquid in the vessel, but as an indication that the oscillations of the liquid occur at very small amplitudes of the oscillations of the vessel. At the resonant frequency, the vessel should not shift at all, since this is the frequency of oscillations of the liquid in a stationary vessel.