In the past few decades, substantial improvements in well-being for a large fraction of the global population have been possible, partly thanks to the exploitation of natural resources. These improvements have been accompanied by large amounts of raw material inflows and outflows of residues/wastes/emissions, which together threaten global sustainability. This study examined some of these sustainability challenges facing current global physical resource management due to the increasing inflows of physical resources to the human activity system and the increasing outflows from that system. For this purpose, the annual production rates and the global resource reserves of 12 natural resources, including major resources for energy (oil, natural gas and coal), agricultural inputs (phosphorus, water and zinc) and industrial production (the rare earth and precious metals) were studied. The results indicate that global reserves of gold, silver, copper, zinc and antimony can sustain their current production rates for only 15-30 years. The longevity of global reserves of oil and phosphorus has increased over the past two decades. The global reserves of natural gas have more than doubled, but the longevity has not increased due to the increasing production rates. Overall, the results show that the global community could simultaneously experience several resource peaks in the coming 30-40 years, leading to inflow-driven economic, technological and social resource supply constraints. They also indicate that the resource supply risks for many resources have not decreased, despite increasing global reserves over the past two decades. In a global context, these findings emphasise the need for recognising and managing the ecological constraints to increasing inflows of physical resources and the outflows of wastes and emissions.