The analysis of stability of the heat conductivity equation with exothermic reaction of zero order and volume-averaged stationary temperature the criteria of thermal explosion of condensed explosive materials (EM) expressions were obtained for parallelepiped, cylinder of finite length and sphere. Estimations of kinetic parameters (frequency factor and thermal decomposition rate activation energy) of HMX and FOX-12 were performed. The numerical solution of thermal conductivity equation for HMX and FOX-12 in the form of cubes was done. A good agreement of the EM ignition criterion in the form of a cube with the available experimental results and numerical solutions of the thermal conductivity equation was obtained. We showed that accounting for the decomposition reaction in the thermal conductivity equation leads to a slight increase in the critical ignition temperature for HMX and FOX-12.