A superconducting winding with a magnetic shield has been studied. The investigations were concerned with the practical application of shielding for magnetic fields higher than 3 T. Tubular magnetic shields have been fabricated with superconducting windings using Nb - Ti multifilamentary composite wire and impregnated with indium (In). With such a design, 3.42 T could be shielded. The characteristics of the shield were: 1, the ability to shield an external field of 3.42 T; 2, the zero field area inside of the shield was relatively broad; and 3, steady, long-term shielding was possible. The origin of the characteristics has been investigated and found to be related to the fact that the current distributions in the shield were induced persistently. In this study, the mechanism of steady magnetic shielding is also reported.