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The ON/OFF method which was developed for the static field problem is extended to the dynamic field problem. We applied the ON/OFF sensitivity method to the steady state linear eddy current problem in order to determine the optimal topology of the electromagnetic and magnetic shield. As a result, a surprising optimal shape of electromagnetic and magnetic shield, which we could not imagine beforehand can be obtained using the ON/OFF method. A criterion of how to choose the sensitivity with respect to the reluctivity or conductivity is discussed. It is shown that the ON/OFF method can be used for the design of electromagnetic or magnetic shielding, even when the material is the magnetic steel sheet which have two kinds of variables, magnetic permeability and conductivity. The best shielding configuration can be obtained for each frequency by adopting the result with a larger design sensitivity.