We use the critical state model to calculate the flux profiles and magnetization curves for type II superconducting hollow cylinders of different wall thicknesses subject to an azimuthal magnetic field produced by a coaxially arranged current-carrying wire. We analyze the cases of field-independent and field-decaying critical current densities, and systematically compare the results with those expected for the conventional slab geometry using parameters typical of a high temperature ceramic superconductor. Some new features are observed for the hollow cylinder, such as the different shape and the asymmetry of the flux distribution profiles, as well as the strong increase of the full penetration field and the field at which the magnetization curves have maxima, with the wall thickness. In our opinion, this feature is the one that should be compared with the experiment in order to test our results.