Using the theory of non classical elastoplasticity with finite deformation theory and the corresponding finite element program,the compression and spring back of an O Ring,the sealing element between flanges of a pressure vessel,was analyzed,and then the relaxation of pressure of the O Ring during cyclic loading and unloading process was investigated.The comparison between the analytical and experimental results is quite satisfactory.It is also showed that the adopted method possesses good convergence and is convenient to engineering application.