The edge fracture of diamond grain plays an important role in cutting-off of stone, concrete and refractory materials. In this paper the edge fracture characteristics of diamond grains are evaluated by the fracture exponents and the edge shape transition probabilities based on the theory of the Markov Process. A grinding test using a single grain permitted the determination of these parameters for two types of synthetic diamonds: MBS and MBS760. As compared with MBS grains, MBS760 grains had low fracture probability and high probability of transition to sharp edges. In the stationary distribution, the existence rates of the sharp edges of MBS760 was about three times higher than that of MBS. Consequently, the application of the theory of the Markov process to the grinding of a hard stone led to a reasonable conclusion that MBS760 was more suitable for grinding hard stones. [ABSTRACT FROM AUTHOR]