Propagation of chemical waves at very low temperatures, observedexperimentally [V.V. Barelko et al., Advances in Chem. Phys. 74 (1988), 339-384.] at velocities of order  10 cm/s, is due toa very non- standard physical mechanism. The energy liberated bythe chemical reaction induces destruction of the material, therebyfacilitating the reaction, a process very different from standardcombustion. In this work we present recent experimental results and develop anew mathematical model which takes into account mechanical and chemicalprocesses. We carry out numerical simulations and suggest a simplified model inorder to obtain an explicit expression for the wave speed. This modelling allowsus to give a possible explanation of the existence of two modes of propagationobserved experimentally and of the dependence of the speed of propagation on theradiation dose.