© 2019, Pleiades Publishing, Ltd. Abstract: A structural based model is proposed to represent the molar volume of silicate melts in terms of both temperature and composition. The model links the molar volume to the internal structure of melts through the concentrations of non-bridging oxygen present in the slag. A previous proposed structural thermodynamic model is used to calculate the content of oxygen ions. The molar volume model requires only one or two parameters to obtain a good agreement between experimental and calculated data for the SiO2–Na2O, SiO2–CaO, SiO2–MgO, SiO2–MnO, and SiO2–PbO binary systems. The molar volume of ternary systems is calculated with the model assuming a linear function of the parameters from binary systems; however, the content of non-oxygen bridges is calculated using the thermodynamic model for ternary systems. Comparison is made between the experimental and model results for the SiO2–CaO–MnO, SiO2–Na2O–PbO and SiO2–CaO–MgO systems.