The paper describes an investigation carried out to determine for three samples of mild steel, (1) the relation between the stress at the yield point in simple tension and in the non-uniform distributions produced by torsion, flexure and internal pressure in a hollow cylinder, and (2) the stress distribution in each of the latter cases in the early stages of overstrain. Apparatus is described for obtaining load-deformation diagrams in which the true resistance to deformation during overstrain is measured. Those obtained for the nonuniform distributions are compared with theoretical diagrams based upon the assumption that a specific shear stress causes the initial breakdown, and that the initial stages of plastic strain take place at a uniform, but lower, shear stress. It is shown that the maximum shear stress at the initial yield point is consistently higher in the non-uniform distributions than in uniform tension. In the cylinders a pronounced scale effect was observed. All the results are consistent with the supposition that the initial dislocation resulting in elastic breakdown takes place at a critical value of the shear stress at a certain depth in the material; in other words, that a surface layer exists possessing the same elastic properties as, but a higher elastic limit than, the interior.