Abstract Ductile behavior of amorphous metals, their ability to sustain localized flow at high nominal stresses, is attributed to a mechanism which alleviates the severe stress conditions prevailing near potential cleavage flaws. The model problem of the plane strain deformation of an infinite block of non-linear visco-elastic material containing an elliptical hole is studied numerically and analytically. A strong dependence of the viscosity on the hydrostatic tension, a result of the increase in the number of viscous flow defects with dilatation, is the principal source of non-linearity. The analysis reveals that, under a constant remote strainrate, the initial elastic stress distribution ahead of the hole gives way, with time, to a more uniform stress distribution. Altering the stress distribution permits the remote (nominal) stress to achieve higher values before critical stress conditions are reached locally at the concentrator. At ordinary temperatures, amorphous metals are not in thermodynamic equilibrium; this motivates a modification of the constitutive law that reflects the kinetic difficulty of maintaining thermodynamic equilibrium under conditions of varying hydrostatic tension. Re-solving the elliptical hole problem with the modified constitutive law reveals a delay in the stress redistribution in front of the concentrator which may explain brittle fracture.