A novel mathematical model to simulate SHS processes is proposed. Based on the so-called enthalpy approach to properly account for phase transitions, the model describes microstructural evolution using suitable population balances. For the case of the synthesis of TiC from pure Ti and C, the model quantitatively interprets that reactants are heated up to the Ti melting point. Once Ti melting occurs, the melt is redistributed within the porous system, thus increasing the contact area between reactants and favoring graphite dissolution. TiC grains are then modelled as nucleating in the melt and then growing until the final microstructure is reached. Model reliability is tested by comparison with experimental data. (C) 2004 Elsevier Ltd. All rights reserved.