The elastic ring is widely used in elastic support structures of aero-engine because of its simple structure and convenient manufacturing. In this paper, two elastic ring models, 3D and 2D models, are proposed, where the fillets between the bulges and ring are considered. The 2D model is more efficient for the calculation of stiffness characteristics. The 3D model can be used to obtain the maximum stress position in the axial direction. Then the experimental testing is carried out to verify the accuracy and effectiveness of the proposed models. Based on the proposed models, the stiffness nonlinearity and critical load of the elastic ring are found for the first time, which can be used to determine the normal working load range. Moreover, the elastic ring models with and without fillets are developed, and the effect of the fillets on stress is discussed. The results show that the stress is reduced by considering the fillets, which are not considered in the existing literature.