Tests have been carried out on thin closed-ended tubes of alpha brass subjected to various combinations of torque and internal pressure. The effect of loading, unloading, and reloading along different loading paths has been investigated, including the effect on the shape of the yield surface, and the form of the curve of representative stress and representative strain. The behavior of the material for initial loading suggests that the material is isotropic in the plane of the surface of the tube but is anisotropic in a radial direction. A form of yield criterion and representative stress which correlates these results has been deduced, but the results of the tests for the second loadings of the specimens cannot be correlated in terms of a nested set of similar yield surfaces. The evidence for or against the existence of corners or pointed vertices on the yield surface is inconclusive.