The definition of a rigorous theoretical framework for the appropriate physico-chemical description of self-propagating high-temperature synthesis (SHS) processes represents the main goal of this work which is presented in two sequential articles. In this article, a novel mathematical model to simulate SHS processes is proposed. By adopting a heterogeneous approach for the description of mass transfer phenomena, the model is based on appropriate mass and energy conservation equations for each phase present during the system evolution. In particular, it takes microstructural evolution into account using suitable population balances and properly evaluating the differentdriving forces from the relevant phase diagram. The occurrence of phase transitionsis treated on the basis of the so-called enthalpy approach, while a conventional nucleation-and-growth mechanistic scenario is adopted to describe quantitatively the formation of reaction products. The proposed mathematical model may be applied to the case of combustion synthesis processes involving a low melting point reactant and a refractory one, as for the synthesis of transition metal carbides from pure metal and graphite. Thus, the model can be profitably used to gain a deeper insight into the microscopic elementary phenomena involved in combustion synthesis processes through a suitable combination of experimental and modeling investigations, as it may be seen in Part II of this work [J. Mater. Res. 20, 1269 (2005)].