With radial coordinate treated as“time”and dual variables introduced, Hamilton’s dual equations can be obtained by using Hellinger-Reissner generalized variational principle. Via introduction of the form of differential FDM into the Radial symplectic system for plane elasticity in polar coordinates and using the difference format instead of differential format in the Hamilton’s dual equations, a Symplectic difference format for plane elasticity in polar coordinates is constructed. so a new FDM under Radial symplectic system is obtained. By soluting the dual equations, displacements and stresses can be obtained directly. The problem of curved beam is calculated by programming. The numerical results show that the new FDM is not only effective but also enrich the method of symplectic FDM.