A computational method is presented for modeling shock-induced chemical reactions (SICR) in multi-material solid powder mixtures. The reacting materials are assumed to be imiscible, which limits the location of the chemical reaction to the material interface between the reactants. This modeling assumption introduces a fundamental difficulty since the product separates the reactants and quenches the reaction. In reality, there is a transport mechanism through the product, however little is known about it other than it doesn't appear to limit the reaction rate. A computational method for overcoming the quenching of the reaction by the product has shown to be promising. It permits distinct descriptions of the particle interfaces and their evolution as the materials within each particle undergo plastic flow, phase transformation, and chemical evolution. An example calculation of the dynamic behavior of the Nb-Si system is presented.