Vertical circular rings and a system of three nested rings are tested and analyzed. The rings are clamped to a flat rigid base and are loaded vertically at the top by either a concentrated load or a rigid plate. The tests involve rings made by 3D printing. In the analysis, each ring is modeled as an inextensible elastica. For downward quasi-static loading, point contact at the base becomes line contact under sufficiently high loads. Deformations are determined, and small vibrations about equilibrium are examined. Good agreement is found between experiments and theory. The topic is motivated by the application of short nested tubes for energy absorption.