jats:pThe propagation of a finite blister of fluid beneath an elastic sheet is controlled by the local dynamics at the peeling periphery of the current. Previous works have described constant volume elastic blisters by considering the peeling due to curvature at these edges. Here, we show that an along-slope component of gravity fundamentally changes the dynamics by removing the role of curvature at the trailing, upslope edge. The local dynamics of this trailing edge is instead controlled by shear stress in the sheet, as in the elastic Landau–Levich problem, and thereby allows for a receding edge, in contrast to propagation by peeling for which only an advancing contact line is possible. Using an asymptotic analysis, we show that this receding edge condition allows for a new, nearly translating regime in which the body of the blister moves at an approximately constant speed, leaving behind a thin layer of fluid. This prediction is verified by detailed numerical modelling of the two-dimensional downslope spreading. We conclude by discussing the applicability of these results in the rapid spreading of subglacial meltwater.</jats:p>