Thin hollow cylinders of Sn In alloys (type II superconductors) have been studied in the field range Hc2 < H < Hc3 where the superconductivity is restricted to a surface layer. With these cylinders both Hc2 and Hc3 are determined independently by resistive and by magnetic measurements. The transitions are much sharper than in the corresponding bulk samples. The resulting Hc3/Hc2 ratio is in good agreement with the theoretical value. Preliminary results on the angular dependence of the upper limiting field have also been obtained.