The torsion of a thin‐walled cylinder is studied using the low‐temperature or visco‐plastic limit of Hart’s state variable theory for the inelastic behavior of metals. For values of the shear stress lower than the ’’hardness’’ of the material, reversible elongation is found to accompany the recoverable twist. For shear stress exceeding the hardness there are, in addition, a permanent twist and elongation. These predictions agree qualitatively with existing experiments. Detailed quantitative results, for several loading histories, are obtained for nickel.