The propagation-mode, compacted-powder. gasless combustion synthesis of intermetallics is modeled through a combined three-scale, particle-level/specimen-level treatment. The specimen-level treatment is based on the local volume-averaged conservation equations for species and energy. The particle-level treatment considers a uniform temperature, the formation of products through a diffusion-controlled heterogeneous reaction, and allows for melting of the product assuming a distinct interface between the phases. The extent of conversion to the final product depends on the local availability of the reactants and through a statistical model and assuming that the interparticle mass transfer resistance is very large, it is determined a priori from the powder particle-size distribution. The influence of the particle-size distribution on the flame structure and the propagation speed is determined using the reaction rate of an average-size particle and also the ensemble average of the reaction rates experienced by particles of different sizes. In a follow-up article (Part II), the results of these models are compared with each other and with experimental results.