The hybrid Cartesian/immersed boundary method is applied to simulate fluid-structure interaction of a two-dimensional orbiting flexible foil. The elastic deformation of the flexible foil is modelled based on the dynamic equation of a thin-plate. At each time step, the locations and velocities of the Lagrangian control points on the flexible foil are used to reconstruct the boundary conditions for the flow solver based on the hybrid staggered/non-staggered grid. To test the developed code, the flow fields around a flapping elliptical wing are calculated. The time history of the vertical force component and the evolution of the vorticity fields are compared with recent other computations and good agreement is achieved. For the orbiting flexible foil, the vorticity fields are compared with those of the case without the deformation. The combined effects of the angle of attack and the orbit on the deformation are investigated. The grid independency study is carried out for the computed time history of the deformation at the tip.