Humans are extracting and consuming unprecedented quantities of materials from the earth's crust. The construction sector and the built environment are major drivers of this consumption which is concentrated in cities. This paper proposes a framework to quantify, spatialise and estimate future material replacement flows to maintain urban building stocks. It uses a dynamic, stock-driven, and bottom-up model applied to the City of Melbourne, Australia to evaluate the status of its current material stock as well as estimated replacements of non-structural materials from 2018 to 2030. The model offers a high level of detail and characterises individual materials within construction assemblies for each of the 13 075 buildings modelled. Results show that plasterboard (7 175 t), carpet (7 116 t), timber (6 097 t) and ceramics (3 500 t) have the highest average annual replacement rate over the studied time period. Overall, replacing non-structural materials resulted in a significant flow of 26 kt/annum, 36 kg/(capita·annum) or 721 t/(km²·annum). These figures were found to be compatible with official waste statistics. Results include maps depicting which material quantities are estimated to be replaced in each building, as well as an age pyramid of materials, representing the accumulation of materials in the stock, according to their service lives. The proposed model can inform decision-making for a more circular construction sector.