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This paper presents and compares two different approaches to the analysis and design of nonferrous shields for extremely low-frequency magnetic fields. The first method is based on a circuital approach where the shield is modeled by a set of conductors coupled with each other by a matrix of self and mutual inductances. The second technique is based on an algebraic formulation of electromagnetic fields and adapted by means of integral equations to the analysis of thin conductive sheets. The paper shows the accuracy of the two methods for calculating induced current density inside the shield and for evaluating magnetic flux density in the shielded region.