The Australian stocks and flows framework (ASFF) is a tool for establishing a coherent historical picture of the Australian physical economy and for testing long-term future scenarios (up to 2050 or even 2100). These scenarios can be used to investigate the long-term physical consequences of current and future choices affecting the physical dimensions of sustainability. In this article we describe the methodology for and construction of a key component of ASFF: a dynamic physical input-output model of material flows in the basic industries. The materials model in ASFF describes physical flows and their transformation by industrial processes. The model's structure permits scenario analysis of long-term technological change by permitting time-varying input-output coefficients and vintage models of capital stocks. As a consequence, the model contains a large number of parameters, which can be left at default settings or adjusted as the modeler sees fit, in order to simulate the widest possible range of physically realizable scenarios. The materials model is built using a methodology that integrates bottom-up process analysis with top-down statistics on material and energy flows. We present some examples showing how the materials model has been implemented to model Australian heavy industries. Several possibilities for further developing the materials model are also described.