Vibrating sample magnetization (VSM) measurements have been made on Fe-clad monocore and multifilamentary MgB2 wire fabricated by the powder-in-Fe-tube technique. The measurements were made with a field sweep amplitude of 17 kOe over a temperature range of 4-40 K. Although the benefits of magnetic shielding to both high-Tc and low-Tc superconductors (SC) have been listed, and in the former case demonstrated, its applicability to the intermediate-Tc material MgB2 is new. Since Fe or low-alloy steels seem necessary primary cladding (sheath) materials for powder-in-tube MgB2 both from mechanical- and chemical-compatibility standpoints, the resulting strands automatically become ideal candidates upon which to explore and exploit the principles of magnetic shielding. The effectiveness of the shield depends on its thickness, relative permeability (and hence strength of the applied field) and shape-dependent demagnetization. In the round monocore wire the SC core was completely shielded against an external field of ±2 kOe; at higher fields a fixed ΔH was observed (partial shielding). Finally, in considering AC loss in the partially shielded regime, allowance must be made for the fact that the signal picked up by the VSM is itself also partially shielded, i.e. reduced in magnitude during its "return passage" through the sheath. FEM calculations of this latter effect are presented. © 2002 Published by Elsevier Science B.V.