The magnetic flux density in the cavity of a sintered tube of Yttrium Barium Copper Oxide (YBCO) is measured as a function of H-parallel to, the axial magnetic field impressed and removed after zero field cooling (ZFC). We note that, in a short thick-walled hollow cylinder of a weak-linked polycrystalline high-T-c superconductor, the magnetic field in the cavity of the tube, H-z hole, rises above the applied field H-parallel to when it is initially increasing. Consequently the standard approach to determine the critical current density from an ascending sweep of H-parallel to alone, or a descending sweep alone cannot be exploited. However the field dependence of the intergranular critical current density J(cm) can be reliably obtained from the horizontal traversals of H-z hole vs H-parallel to. Comparison of the experimental data with model calculations for the horizontal traversals of the hysteresis curves show that the intergranular critical current density in the YBCO tube has a Kim-like field dependence. The magnetization of the grains has a significant influence on the flux density in the cavity of the tube. (c) 2006 Elsevier B.V. All rights reserved.