This paper is a report on experiments with the torsion of rectangular mild-steel tubes undertaken to test the correctness of the now generally accepted theory of R. Bredt, based on a hydrodynamical analogy. The angles of torsion were determined, and the strains were measured with Huggenberger tensometers. While most of the strains were measured on the external surface of the tubes, internal strains were measured in one tube. The observed angles of torsion were found to be in fair agreement with the theory, but the shearing stresses on the external surface were much higher and those on the internal surface much lower than the theoretical stresses. Breakdown of the tubes occurred while the theoretical shearing stress was still far below the yield point in shearing of the material. It appears that the theory does not give a true picture of the stress distribution after plastic flow has occurred at the re-entrant corners, and as this may happen very early, dependent on the radius of the fillets, the theory may in some cases lead to a dangerous overestimate of the strength of such tubes.