The recent acceleration of urbanization and industrialization of many parts of the developing world, most notably in Asia, has resulted in a fast-increasing demand for and accumulation of construction materials in society. Despite the importance of physical stocks in society, the empirical assessment of total material stock of buildings and infrastructure and reasons for its growth have been underexplored in the sustainability literature. We propose an innovative approach for explaining material stock dynamics in society and create a country typology for stock accumulation trajectories using the ARIMA (Autoregressive Integrated Moving Average) methodology, a stochastic approach commonly used in business studies and economics to inspect and forecast time series. This enables us to create scenarios for future demand and accumulation of building materials in society, including uncertainty estimates. We find that the so-far overlooked aspect of acceleration trends of material stock accumulation holds the key to explaining material stock growth, and that despite tremendous variability in country characteristics, stock accumulation is limited to only four archetypal growth patterns. The ability of nations to change their pattern will be a determining factor for global sustainability.