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A novel approach for analyzing conducting shields of extremely low frequency magnetic fields in linear media is presented. It consists of an integral formulation based on the cell method, expressed in terms of network-like loop currents and magnetic vector potential line integrals on the shield surface. This formulation leads to a considerable reduction of field problem variables, thus limiting the amount of allocated memory and speeding-up the numerical procedure compared to other differential and integral techniques. Eddy currents are computed first, then the magnetic vector potential and the magnetic flux density distributions are evaluated by applying the superimposition principle. A detailed comparison between this method and a three-dimensional finite element method code demonstrates the accuracy of the results and the advantages of the method.