The stresses and displacements in a partly plastic, infinitely long, hollow cylinder are obtained according to the flow type of stress-strain law of Prandtl-Reuss and to the deformation law of Hencky. In both cases the Mises yield condition is used and the compressibility of the material is taken into account. It is shown that under these assumptions the two theories yield substantially the same results for this particular problem, but that one theory or the other may be preferable for computing purposes in certain cases. The results are compared with those of other investigations in which different combinations of stress-strain law, yield condition, compressibility, and end loading were assumed.