Ring-mold craters (RMCs), concentric crater forms shaped like a truncated torus and named for their similarity to the cooking implement, are abundant in lobate debris aprons (LDA) and lineated valley fill (LVF) in the northern mid-latitudes on Mars, but are not seen in surrounding terrain. LDA and LVF have been interpreted to form by flow of debris, but uncertainty remains concerning the mechanism of flow, with hypotheses ranging from pore-ice-assisted creep of talus to debris-covered glaciers. RMCs average less than a few hundred meters in diameter and occur in association with normal bowl-shaped impact craters whose average diameters are commonly less than RMCs. On the basis of their morphologic similarities to laboratory impact craters formed in ice and the physics of impact cratering into layered material, we interpret the unusual morphology of RMCs to be the result of impact into a relatively pure ice substrate below a thin regolith, with strength-contrast properties, spallation, viscous flow and sublimation being factors in the development of the ring-mold shape. Associated smaller bowl-shaped craters are interpreted to have formed within a layer of regolith-like sublimation till overlying the ice substrate. Estimates of crater depths of excavation between populations of bowl-shaped and ring-mold craters suggest that the debris layer is relatively thin. These results support the hypothesis that LDA and LVF formed as debris-covered glaciers and predict that many hundreds of meters of ice remain today in LDA and LVF deposits, beneath a veneer of sublimation till. RMCs can be used in other parts of Mars to predict and assess the presence of ancient ice-related deposits.