The shielding effect of electrically conductive materials is based on field reflection caused by induced eddy currents in the material. However, this mechanism does not work at low frequencies, thus non-magnetic materials like copper or aluminium are almost ineffective against low-frequency or static magnetic fields.
To effectively shield static or low-frequency magnetic fields, ferro-magnetic materials are used. Compared to air, they have a magnetic conductivity (permeability) which is several orders of magnitude higher. The field is redirected through the magnetic material and the field strength in the inner of a magnetically shielded space is significantly reduced.
The shielding factor S is the ratio between the outer field Ba and the inner field Bi in a shielded space. For a closed cylindrical shielding in a transverse field, the following formula can be used as an approximation:
S = µ * d / D
where µ = relative permeability, d = wall thickness and D = diameter of the cylinder.
Real shielding problems can rarely be solved by analytic methods. Also FEM simulations often yield significant deviations from reality.