In this study, Ca, Mg, Al, and Pb concentrations leached from uncarbonated and carbonated ordinary Portland cement – dried waste incinerator bottom ash samples during single extraction tests (EN12457 test) at a pH from 1 to 12, were modelled using the geochemical code PHREEQC. A good agreement was found between modelling results and experiments in terms of leached concentrations for Ca, Mg, and Al by defining a single set of pure mineralogical phases for both the uncarbonated and carbonated (three levels) samples. The model also predicted well the observed decrease in Ca leaching with increasing carbonation. Modelling results further revealed that leaching of Pb is not controlled by dissolution/precipitation of pure Pb containing minerals only (carbonates and (hydr)oxides). The addition of solid solutions (calcite-cerrusite and gibbsite-ferrihydrite-litharge solid solutions) and adsorption reactions on amorphous Fe- and Al-oxides improved the model representation of the experimentally observed amphoteric leaching profile of Pb from the cementitious material.