•Conceptual clarifications of stock-flow dynamics for stock saturation hypothesis.•Limited empirical support for already occurring stock saturations.•Until 2035, first signs of potential saturations in some industrialized regions.•China massively drives global stock-flow dynamics since the 1990s.•Radically improved stock-flow management vital to reduce material use. Material stocks in infrastructure, buildings and machinery shape current and future resource use and emissions. Analyses of specific countries and selected materials suggest that material stocks might saturate, which would be important for a more sustainable social metabolism. However, it is unclear to what extent the evidence holds for a wider range of stocks and flows, as well as for world regions or globally. We present an inflow-driven dynamic stock-flow model for 14 bulk materials, end-of-life outflows, recycling, and waste flows for nine world regions from 1900 to 2015, extended with trend scenarios until 2035. Material stocks are growing in all regions and show little signs of saturation yet. In 2015, China used half of global stock-building materials, overtook everyone in stock size around 2012 and grows its stock at ∼8%/year. The Industrialized regions, including the Former Soviet Union, are slowly expanding their high stock levels at ∼1%/year. Stocks in all other regions, inhabited by 60% of the world population, grow at ∼3–5%/year. Inequalities in per capita stocks between regions are large. Trend scenarios suggest potential absolute or per capita stock saturations in some of the industrialized regions, while all other regions are expected to continue high stock growth. Accumulated stocks drive future end-of-life materials and substantial maintenance and replacement requirements. Growing material stocks hamper a potential stabilization or reduction of resource use. Low stock levels in most world regions suggest a crucial window of opportunity for avoiding resource-intensive stock development. In the industrialized regions and especially China, stabilising and reducing resource use requires halting net stock expansion and transforming existing stocks. More materials- and energy-efficient and long-lived stocks which deliver high quality services, and improved reuse, repair and recycling of increasing end-of-life materials to close loops and actually replace virgin resources, are crucial for a more sustainable social metabolism.