Experiments have been carried out on the flux trapping and shielding capabilities of tubular superconductors in transverse dipole and quadrupole fields. Field profile measurements are reported for tubes of vapor-deposited Nb3Sn and samples assembled from spirally wound strips of Nb-Ti/Cu sheet composite. The flux trapping and shielding process is modeled by assuming that critical state currents flow in saddle-shaped paths in the sample walls. Good correspondence between the experimental and model-generated field profiles is achieved. The model can be used in the design or analysis of flux trapping and shielding devices, or to obtain estimates of the average critical current density from measurements of the trapping or shielding ability of tubular samples.