It is shown how group-theoretic methods, or similarity methods, can be applied to determine the class of self-similar solutions for a one-dimensional, time-dependent problem in shock hydrodynamics,with a chemical reaction taking place behind the shock. The functional form of all reaction rates depending on the state variables is characterized under which the general system of differential equations and boundaryconditions admit self-similar solutions, It is shown that a subclass of these solutions can model certain processes in detonation physics.