Abstract <p>A refined mathematical model of a cylindrical hydrodynamic suspension is proposed with full consideration of the dependence of the velocity distribution profile of the liquid on the radial coordinate in the supporting layer, which more fully takes into account the influence of viscous friction forces. On the basis of the proposed model, the stability of the suspension is investigated using the frequency criterion of stability of hybrid dynamic systems. A suspension with a light inner body, the reduced density of which is less than the density of the supporting layer, is asymptotically stable near the central position, and remains stable over a large range of changes in relative eccentricity. The use of a refined mathematical model leads to a greater margin of stability and a shorter transition time for suspension with a light inner body. An increase in the angular velocity of rotation of the outer cylinder leads to a significant decrease in the characteristic values of the displacements of the inner cylinder. In&#xa0;this case, a suspension with a light inner body has a large margin of stability and remains operational under significant external overloads. A suspension with a heavy inner body, the reduced density of which is greater than the density of the supporting layer, is unstable near the central position. When it is displaced from the central position along the curve of mobile equilibrium, a stability region may occur, but the stability margin of the suspension with a heavy internal body is insignificant.</p>