The continuum modeling of finite element method is used to study the fully nonlinear plastic failure of the transverse ring structure of a ship. By using this finite element discretization, the connection portions of structural members can be treated as two-dimensional deformable bodies. This can contribute to the accounts of stress concentration and continuum development of plastic zones, which can better represent local and global mechanics behaviors and accurately predicts the fully nonlinear plastic failure of the transverse ring structure. The incremental/iterative procedure is used to update the response histories of the related nonlinear finite element systems. And an accelerated iteration method, proposed by the present author, based on improving a modified Newton-Raphson scheme is used to obtain converged solutions of the discretized nonlinear algebraic systems. In analyzing the transverse ring structure of a ship, the response history is updated up to a close fully nonlinear plastic failure load stage. The mechanics behaviors of the structural members are studied.