Propagation of chemical waves at very low temperatures, observed
experimentally [V.V. Barelko et al., Advances in Chem. Phys. 74 (1988), 339-384.] 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.