The locations and extent of mountain glaciers are affected by climatic constraints such as air temperature, precipitation, and solar radiation, as well as by local topography, which influences avalanche accumulation and debris supply. To evaluate these influences on the elevational distribution of glaciers in the Bhutan Himalaya, we created a glacier inventory together with debris-covered area and potential material-supply (PMS) slopes using satellite images with high spatial resolution. The median elevation of a glacier, which is used as a proxy of the equilibrium line altitude (ELA), decreases with increasing annual precipitation, suggesting the influence of climatic factors, according to which the ELA is lowered in relatively warm and humid environments, and raised when the opposite conditions prevail. We found a weak but significant influence of topography on the elevational distribution of glaciers, indicated by the relationship between the deviation of the median elevation of an individual glacier from the regional average and the PMS slope ratio (defined as the ratio of the PMS slope area to glacier area). We further analysed the dependency of the median glacier elevation on the gradient and aspect of PMS slopes. We found that the median elevation is affected by the avalanche-driven redistribution of snow accumulation on debris-free glaciers, and that in debris-covered glaciers the debris supply affects glacier extent through the insulation effect of the debris layer.