Full-thickness crevasses can transport water from the glacier surface to the bedrock where high water pressures can open kilometre-long cracks along the basal interface, which can accelerate glacier flow. We present a first computational modelling study that describes time-dependent fracture propagation in an idealised glacier causing rapid supraglacial lake drainage. A novel two-scale numerical method is developed to capture the elastic and viscoelastic deformations of ice along with crevasse propagation. The fluid-conserving thermo–hydro–mechanical model incorporates turbulent fluid flow and accounts for melting and refreezing in fractures. Applying this model to observational data from a 2008 rapid-lake-drainage event indicates that viscous deformation exerts a much stronger control on hydrofracture propagation compared to thermal effects. This finding contradicts the conventional assumption that elastic deformation is adequate to describe fracture propagation in glaciers over short timescales (minutes to several hours) and instead demonstrates that viscous deformation must be considered to reproduce observations of lake drainage rates and local ice surface elevation changes. As supraglacial lakes continue expanding inland and as Greenland Ice Sheet temperatures become warmer than −8 °C, our results suggest rapid lake drainage events are likely to occur without refreezing, which has implications for the rate of sea level rise.