A new, more accurate formula describing double and multiple-shell axial magnetic shielding is obtained as a result of numerical verification of existing estimations. A standard ANSYS® software package was used. Parameters of the numerical model are as follows. Two concentric, closed cylinders of equal thickness and constant permeability are considered. The thickness-to-diameter ratio of the outer cylinder is t/D2=1/100, its length-to-diameter ratio varies as L2/D2=3, 4, and 5, the ratio of the cylinders’ outer diameters varies as D1/D2=0.5, 0.6, 0.7, 0.8, and 0.9, a range of the ratio of the cylinders’ lengths is L1/L2=0.1–0.9, and a range of the relative permeability is μ =103–106. A significant disagreement between the existing estimations and between each of them and the numerical model is found. One of the examined algorithms is modified to improve its precision. A remarkable improvement in the accuracy of the new algorithm compared to both existing methods is achieved. On a basis of the new algorithm, a new formula describing multishell axial magnetic shielding is suggested.