The analogue of the surface nucleation field H_c3 is calculated for a superconducting cylinder in a magnetic field parallel to its axis. For small radius, on the scale of the coherence length, superconductivity nucleates uniformly across the cylinder, while for large radius a surface sheath nucleates at the outer perimeter, the bulk of the cylinder remaining normal. The transition between these two limits is seen as a succession of flux entry points each corresponding to an increase by unity in the magnitude of the fluxoid quantum number.