An exact calculation is given of the upper critical field of a hollow isotropic type-II superconducting cylinder. This field is the analogue of the surface-sheath critical field H_c3. As the temperature decreases below T_c the critical field corresponds to increasing values of the azimuthal quantum number mod m mod , i.e. the fluxoid number. The results are compared with those for a flat surface, a film and a solid cylinder and with the approximate result for a thin-walled cylinder. For the last case, it is shown bow the Little-Parks oscillations are modified as the cylinder wall thickness increases. The effects of normal-metal cladding on the inner and outer surfaces are calculated.