The magnetic shielding by the heat‐treated superconducting Nb‐40 at.% Zr‐10 at.% Ti hollow cylinder, 5 mm in inner diameter, 9 mm in outer diameter, and 25 mm in length, was investigated at 4.2°K in applied axial magnetic field. The dependence of the magnetic shielding capacity upon the field rate of increase was examined for the samples subjected to the solution treatment at 1100°C for 5 h in vacuum of 10−6Torr and to the heat treatment at 700°C for 3, 10, and 100 h after solution treatment. The magnetic shielding capacity of the sample, heat treated at 700°C for 100 h, was over 17.5 kOe as the magnetic field was applied with its rate of increase of 0.45 kOe/min. A possible phenomenological model estimating the maximum or minimum magnetic shielding capacity was developed by assuming that the flux front in the Bean critical state moves isothermally or adiabatically toward the interior of the hollow cylinder. The calculated value agreed well with the measured value for each sample.