Bonded ice crystals under pressure are in a heterogeneous stress state because of the mechanical anisotropy of constituent grains. This condition plays a role in intergranular melt and recrystallization, which in turn influence properties such as permeability and biologic habitability. To examine this, we develop an anisotropic elastocreep model simulating subgrain-scale stresses in polycrystalline ice, choosing in particular the thermal and deformational regime of the Lake Vostok accretion ice. A critical assumption with regard to localized melting is the macroscopic deviatoric stress. Our calculations indicate that for a macroscopic deviatoric stress of 50 kPa, ice at 0.04°C below the bulk melting temperature would contain regions, at scales ∼1% the grain size, where the liquid phase is thermodynamically favored. This translates to scales of ∼5 mm in the lower few meters of the Vostok accretion under a deviatoric stress that is plausible near the lake perimeter. Less internal melting is indicated in analyses of ice relatively far from the lake margins due to the assumed presence of lower macroscopic deviatoric stress. Simulated strain energy jumps of 1–2% across grain boundaries of accretion ice near the lake boundaries are large relative to free surface energy, indicating the importance of the former in boundary migration recrystallization. Collectively, these findings are consistent with measured dislocation densities (>10⁷–10¹⁰ m⁻²) and irregular grain morphologies found in core samples. The calculated melting point depressions associated with anisotropy fall short of experimental values by a factor of ∼2, while the calculated strain rates deviate by ∼20%.