[en] We report on a combined experimental and modelling approach towards the design and fabrication of efficient bulk shields for low-frequency magnetic fields. To this aim, MgB₂ is a promising material when its growing technique allows the fabrication of suitably shaped products and a realistic numerical modelling can be exploited to guide the shield design. Here, we report the shielding properties of an MgB₂ tube grown by a novel technique that produces fully machinable bulks, which can match specific shape requirements. Despite a height/radius aspect ratio of only 1.75, shielding factors higher than 175 and 55 were measured at temperature T = 20 K and in axially-applied magnetic fields μ ₀ H _appl = 0.1 and 1.0 T, respectively, by means of cryogenic Hall probes placed on the tube’s axis. The magnetic behaviour of the superconductor was then modelled as follows: first we used a two-step procedure to reconstruct the macroscopic critical current density dependence on magnetic field, J _c(B), at different temperatures from the local magnetic induction cycles measured by the Hall probes. Next, using these J _c(B) characteristics, by means of finite-element calculations we reproduced the experimental cycles remarkably well at all the investigated temperatures and positions along the tube’s axis. Finally, this validated model was exploited to study the influence both of the tube’s wall thickness and of a cap addition on the shield performance. In the latter case, assuming the working temperature of 25 K, shielding factors of 10⁵ and 10⁴ are predicted in axial applied fields μ ₀ H _appl = 0.1 and 1.0 T, respectively. (paper)