A simple model is presented which describes the propagation of chain reactions in amorphous solids. It is developed within the framework of a self-avoiding random walk on a Bethe lattice. Simple analytical formulae are obtained for the average chain lengths and chain length distributions. These are compared with computer simulations of solid state chain reactions on three dimensional lattices and with recent experimental results. The model can describe chain reactions in pure solids (e.g., polymerization of solid formaldehyde at 10 K) as well as chain reactions in binary solid solutions (e.g., reaction of Cl₂, with cyclopropane deposited as a van der Waals glass at 77 K). The predicted dependence of reaction chain length on the relative concentrations of the two reactants is in good accord with experimental results.