To assess the role of thermal contraction-crack polygons (sublimation polygons) in modulating sublimation of buried glacier ice in Antarctica, we applied a 2D numerical model using COMSOL Multiphysics that calculates the rate and spatial variability of vapour diffusion through porous media. Specifically, we examined vapour transport through Granite drift, a dry supraglacial till marked with thermal contraction-crack polygons that rests on glacier ice reportedly ≥8-million years in age. The model results show that sublimation varies with drift texture and surface topography. Initially, the rates are highest beneath relatively coarse-grained sand-wedge deposits at polygon margins, creating deep, surface troughs. As troughs approach ~1-m depth, the cooler atmospheric and soil temperatures that arise from solar shielding reduce the rates of ice sublimation to levels below that at polygon centres, preventing runaway ice loss at polygon margins. Including the effects of a salt-cemented horizon at 10 − 15-cm depth (porosity 20%) and a rocky surface pavement (75% ground coverage), our modelled ice loss at polygon centres, for example, is 0.022 mm a−1, an order of magnitude lower than previous estimates (0.14 mm a−1). This finding highlights the importance of including field-based data for drift texture, topography and microclimate variation in modelling ice sublimation. The results also suggest that stable conditions (no ice loss) at polygon centres are possible with either a 1.9°C decrease in mean annual atmospheric temperature or a 12 per cent increase in mean annual relative humidity. These results indicate that the preservation of buried, multi-million-year-old ice is plausible in the coldest and driest regions of Antarctica. Copyright © 2011 John Wiley & Sons, Ltd.