AbstractRock debris on the surface of ablating glaciers is not static, and is often transported across the ice surface as relief evolves during melt. This supraglacial debris transport has a strong influence on the spatial distribution of melt, and is implicated in the formation of hummocky glacial topography in deglaciated terrain. Furthermore, as ice‐dammed lakes and ice‐cored slopes become increasingly common in deglaciating watersheds, there is rising concern about hazards to humans and infrastructure posed by mass‐wasting of ice‐cored debris. The existing quantitative framework for describing these debris transport processes is limited, making it difficult to account for transport in mass balance, hazard assessment, and landscape development models. This paper develops a theoretical framework for assessing slope stability and gravitational mass transport in a debris‐covered ice setting. Excess water pressure at the interface between ablating ice and lowering debris is computed by combining Darcy's law with a meltwater balance. A limit‐equilibrium slope stability analysis is then applied to hypothetical debris layers with end‐member moisture conditions derived from a downslope meltwater balance that includes production and seepage. The resulting model system constrains maximum stable slope angles and lengths that vary with debris texture, thickness, and the rate of meltwater production. Model predictions are compared with field observations and with digital elevation model (DEM)‐derived terrain metrics from two modern debris‐covered glaciers on Mount Rainier, USA. Copyright © 2017 John Wiley & Sons, Ltd.