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It has been predicted theoretically that, in general, a right‐circular cylinder of incompressible, highly elastic material, which is isotropic in its undeformed state, cannot be held in a state of pure torsional deformation by means of a torsional couple alone. In addition, normal surface tractions must be exerted over the plane ends of the cylinder. These normal surface tractions depend on the amount of torsion and on position on the plane ends of the cylinder. Experiments are reported here in which this phenomenon is observed in a right‐circular cylinder of pure gum compound. The dependence of the surface traction on amount of torsion and its distribution over the surface of the cylinder is studied by measuring the bulging of the rubber into small holes in a metal plate on one end of the cylinder.