Petroleum companies and Arctic states are carefully watching the sea ice withdrawal and the future access to petroleum resources in the Arctic. We raise the question if the global market for petroleum will actually keep the door open for substantial supply of oil and gas from the Arctic, a region with almost a quarter of global undiscovered petroleum resources, but at high costs and long lead times. This makes future Arctic supply highly dependent on oil and gas prices, influenced by future supply of unconventional oil and gas and also by huge amounts of conventional gas in the Middle East coming on stream. We study the oil and gas supplies from 6 Arctic regions during 2010–2050 using the FRISBEE model of global oil and gas markets, based on Arctic resource estimates from the U.S. Geological Survey. Following the IEA reference oil price assumption, we find that even if almost a quarter of the world's undiscovered petroleum is situated in Arctic basins, the future share of global production will only be 8–10% in our reference scenario. Although a major part of the undiscovered Arctic resources is natural gas, the relative importance of the Arctic as a world gas supplier will decline, while its relative importance as a global oil producer might be maintained. Less undiscovered oil resources will have minor effect on total Arctic oil production and a marginal effect on Arctic gas extraction as Arctic Russia is the dominant petroleum producer with a sufficiently large stock of already discovered resources at relatively low costs to support their petroleum production before 2050.