A translational gauge approach of Einstein type was proposed for obtaining the stresses that were due to non-singular screw dislocations. The stress distribution of the second order around the screw dislocation was classically known for the hollow circular cylinder with traction-free external and internal boundaries. The inner boundary surrounds the dislocation's core, which was not captured by the conventional solution. The present gauge approach permitted the continuation of classically known quadratic stresses to within the core. The gauge equation was chosen in the Hilbert–Einstein form, and it played the role of non-conventional incompatibility law. The stress function method was used, and it led to the modified stress potential given by 2 constituents: the conventional one (the background) and a short-ranged gauge contribution. The latter simply caused additional stresses, which were localized. The asymptotic properties of the resulting stresses were studied. Since the gauge contributions were short-ranged, the background stress field predominated sufficiently far from the core. The outer cylinder's boundary was traction-free. At sufficiently moderate distances, the second-order stresses acquired regular continuation within the core region, and the cut-off at the core did not occur. Expressions for the asymptotically far stresses provide self-consistently new length scales dependent upon the elastic parameters. These lengths could characterize the exterior of the dislocation core region.

The Einsteinian T(3)-Gauge Approach and the Stress Tensor of the Screw Dislocation in the Second Order - Avoiding the Cut-Off At the Core. C.Malyshev: Journal of Physics A, 2007, 40[34], 10657-84