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The thickness of thin cylindrical copper shells of radius and thickness were measured by means of an inductive measurement. The samples were obtained by chemical reduction of thick copper pipes. The conductivity of the cylinders was measured by a standard four-terminal technique. The agreement between the value of thickness measured mechanically and the value obtained from inductive measurement is of the order of ±2 percent. Thicker brass shells were measured and these results compared with theory. The extension of the inductive measurement to cylindrical shells covering cylinders with a finite conductivity is also discussed.