The thermal decomposition of an explosive material is accompanied by generation of a certain amount of heat and, under certain conditions, can lead to the well-known phenomena of self-ignition. Therefore, it is of great importance to predict whether or not an explosive material will ignite under given conditions (specimen mass and shape, surrounding temperature, etc.). An own computer program named THERMEX, for studying thermal ignition phenomena, is discussed in this paper. The program uses the finite difference method to describe the reactive heat conduction phenomena in infinite slab, cylindrical, and spherical geometry of explosive materials. The analysis of the stability requirements of the finite difference method applied in the program is carried out. The program is tested by the comparison of calculated results with the results of calculation by other authors. Reasonable agreement was found under identical computational conditions.