The superconducting solenoid magnet for high energy physics or the MRI systems use the iron shield to enhance the central field or tb shield the strong leakage magnetic field. But the design technique of the iron shape has not been established, since the iron has nonlinear permeability. In the present paper, a optimizing procedure of the iron shield shape is proposed. Our procedure is based on the hybrid finite element-boundary element method (HFB method). The HFB method is suited to analysis of problem which present nonlinear behavior and extend to infinity. The HFB method may facilitate to optimize the shape of the nolinear iron shield.
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