This paper develops a theoretical model of material flow analysis (MFA) within the framework of the Waste Input–Output model (WIO) (Nakamura and Kondo). The model is developed based on two fundamental ingredients: yield ratios and the degree of fabrication. In manufacturing process, multiplication of physical inputs by the yield ratios gives the portion that enters physical outputs, with the rest being discarded as process waste without entering outputs. In input–output analysis, the degree of fabrication can be visualized as triangularity of the input coefficients matrix (goods of lower degree of fabrication can enter those of higher fabrication, but the reverse does not hold), which is known to emerge through an appropriate reordering of sectors. Application to the Japanese IO data indicates that the model can provide accurate estimates of the weight as well as the composition of metals (Fe, Cu, Pb, Zn, and Al) used in a passenger car. The model is also used to estimate the major final use categories (household consumption, public consumption, capital investment, inventory investment, and export) of metals.