The same property of the phase transformations driven by short range diffusion (recrystallization, allotropic transformation, grain coarsening) is that the movements of the grain or the phase boundaries take place by atomic jumps through the boundaries. The probability (frequency) of these jumps depends on only on the energy state of the closenear neighborhood of the atoms. In the operation of cellular automata Consequently, only the closenear neighborhood of the cells is taken into account in the operation of the cellular automaton. This similarity makes applicable the cellular automaton applicable to simulate the aforementioned phase transformation processes. A condition (rule) of the movement of grain and phase boundaries is introduced, which makes it possible to simulate all the all mentioned phase transformation by the same automatona.