Recently obtained geophysical data show sets of parallel erosional features on the Lomonosov Ridge in the central Arctic Basin, indicative of ice grounding in water depths up to 1280 m. These features have been interpreted as being formed by an ice shelf-either restricted to the Amerasian Basin (the "minimum model") or extending across the entire Arctic Basin. Here, we use a numerical ice sheet-shelf model to explore how such an ice shelf could form. We rule out the "minimum model" and suggest that grounding on the Lomonosov Ridge requires complete Arctic ice shelf cover; this places a minimum estimate on its volume, which would have exceeded that of the modern Greenland Ice Sheet. Buttressing provided by an Arctic ice shelf would have increased volumes of the peripheral terrestrial ice sheets. An Arctic ice shelf could have formed even in the absence of a hypothesised East Siberian Ice Sheet.