AbstractIt is shown that a passive magnetic shield for a 1,5‐T whole‐body magnet requires about 20 tons of iron. Moreover, to first order, the amount of shielding material is independent of the radius of the shield. The choice between a thick shield fitting tightly round the magnet and a thinner shield of larger radius is determined by considerations of available space and the need for the highest uniformity of field in the bore. Very high permeability materials such as mu‐metal are useful only in special circumstances. Multiple shields are valuable if a high degree of shielding is required, but the spacing between the shields needs careful attention. Although exact reciprocity of internal and external shielding is not found in the general case, the degree of shielding will be of the same order in both cases. The complete behavior of cylindrical shields around superconducting magnets can be determined by analytical solution of Maxwell's equations; for less regular shapes, solutions may be determined numerically by computer. © 1991 Academic Pres