Abstract. Propagation of chemical waves at very low temperatures, observed experimentally [1] at velocities of order 10 cm/s, is due to a very non-standard physical mechanism. The energy liberated by the chemical reaction induces destruction of the material, thereby facilitating the reaction, a process very different from standard combustion. In this work we present recent experimental results and develop a new mathematical model which takes into account mechanical and chemical processes. We carry out numerical simulations and suggest a simplified model in order to obtain an explicit expression for the wave speed. This modelling allows us to give a possible explanation of the existence of two modes of propagation observed experimentally and of the dependence of the speed of propagation on the radiation dose.