Previous empirical studies assessing sustainability have adopted the weak sustainability indicator (WSI) which measures changes in the stock of physical and natural capital. Whereas these studies have been retrospective, we use a dynamic general equilibrium model to investigate global and regional sustainability over the period 1985–2050, focusing on fossil fuel extraction. Our standard scenario predicts increasing WSI values suggesting global sustainability in all periods to 2050 as, despite a rising world oil price, the introduction of backstop fuels in 2010 provides an alternative source of energy. A more pessimistic scenario examines possible outcomes in the absence of energy saving technological change and backstops fuels. WSI values still indicate global sustainability, though economic growth is only half that predicted by the more optimistic model, and two countries—USA and Brazil—are unsustainable.