The critical phenomena determining the propagation of an adiabatic shear band occur at its extremity. The stress and strain distributions at the tip of a shear band are calculated as a function of applied shear strain using the finite element method for an elasto-plastic material. Three assumptions simplify the calculations considerably: (a) the mechanical response of the material follows an adiabatic stress-strain curve; (b) the material within the shear band has zero shear strength; (c) the body is taken to be in equilibrium. The distribution of stresses and strains in the adiabatically-deformed material is compared to that of a quasi-statically deformed material. While the stress-strain curve for an isothermally deformed material is monotonic with continuous work-hardening, the adiabatic work-hardening curve reaches a plateau followed by work-softening (due to thermal softening). The stress and strain fields for both cases are nearly identical, except in the region directly in front of the shear band. In the adiabatically-deformed material a thin region (~5 μm) with large strains and lowered stresses is produced. This region, in which accelerated deformation takes place as the applied shear deformation increases, is absent in the isothermally-deformed material. The formation of this instability region, ahead of the shear band, is considered to be the mechanism for the propagation of an adiabatic shear band.