During the summer of 2010, the presence of a pressurized water-filled subglacial-cavity of at least 50,000 m3 was detected within the Tête Rousse Glacier (French Alps). Artificial drainage was started to avoid an uncontrolled rupture of the ice dam, but was interrupted soon after to evaluate the capacity of the cavity-roof to bear itself. The risk was that the release of pressure within the cavity during the artificial drainage would precipitate the collapse of the cavity roof and potentially flush out the remaining water flooding the valley below. An unprecedented modeling effort was deployed to answer the question of the cavity roof stability. We set up a model of the glacier with its water cavity, solved the three-dimensional full-Stokes problem, predicted the upper surface and cavity surface displacements for various drainage scenarios, and quantified the risk of the cavity failure during artificial drainage. We found that the maximum tensile stress in the cavity roof was below the rupture value, indicating a low risk of collapse. A post drainage survey of the glacier surface displacements has confirmed the accuracy of the model prediction. This practical application demonstrates that ice flow models have reached sufficient maturity to become operational and assist policy-makers when faced with glaciological hazards, thus opening new perspectives in risk management of glacier hazards in high mountain regions.