Radial stiffness of flexible ring dampers used in rotor supports is analyzed in this paper. Two major approaches are proposed for this purpose. The first is the conventional finite element modeling of this contact mechanics problem. The second is an analytical method that can be used as alternative to the costly numerical computations. This method is based on the Kalker’s principle of minimum complementary energy. A special variational formulation is developed in the closed form using Euler–Bernoulli beam approximation for the elastic ring and a simplified model of normal contact at the ring flanges. It has been shown that the surface tolerances of the parts have a substantial effect on the radial response of the flexible ring that may become nonlinear. The tight fit of the ring on both sides makes it much stiffer, while the loose fit results in free motion of the rotor and much weaker damping of its motion. Both methods produced results that are in excellent agreement for the considered cases.