The use of bulk MgB 2 as a magnetic shield may have interesting applications in the accelerator field as magnetic protection of the particle beams. Many of these applications will require a low-temperature environment due to the high magnetic fields involved; therefore, the stability of superconducting bulk materials, at these low temperatures, must be carefully controlled. Critical stability issues of the bulk superconducting materials include macro- and micro-flux jumps, which are related, respectively, to the sudden loosing of the shielding effect and to the initial reduction of the shielding characteristic, which initiates the long-term relaxation phenomena. We have tested the shielding characteristics at 4.2 K of a bulk MgB 2 tube (L = 450 mm, OD/ID = 49/32.4 mm), produced by the reactive liquid infiltration process that is capable to reduce to a minimum the macro-flux jumps. Applying step-wise increasing transverse magnetic fields up to about 3 T on the surface of the tube, we measured the dynamics of the superconducting currents that, with their displacements, give rise to the relaxation phenomena. These effects have been modeled by the superposition of two exponential decay functions. This parametrization can help in the prediction of the magnetic behavior of this material, but in a limited time lapse.