Fish farming in the open ocean is becoming a dominant form of fishery aquaculture due to the dramatic drop of fishery resources in near shore. Deep water anti-stormy fish cages are the most important tool for fish farming in the open ocean. The floatation ring, as a pivotal component of the fish cage, undergoes large deformations and it has been found that the floatation ring oscillates when moving in water waves. In the most serious cases, its deformation is so large it can be damaged. The floatation ring is simplified as a free circular ring, and the governing equations of motion and deformation of the ring can be built up according to the force equilibrium and curved beam theory. The numerical calculation is carried out in terms of the modal superposition method. The motion and the deformation of the ring are analyzed, and two corresponding equations in which the elastic deformations are neglected and considered are given, respectively. By comparing the results of the above two equations, we get the resonant frequencies and the frequency scope influenced by the elastic deformation. It is concluded that the influence of the deformation of the ring is very important for the oscillation of the ring, particularly the former three modes of the elastic deformation which cannot be neglected.