As a cleavage crack propagates through a field of randomly oriented grains, due to the variation in local fracture resistance, the crack front advance is nonuniform. The crack would first penetrate into the low-toughness grains, leaving the high-toughness ones behind its front. In this article, the barrier effect of the high-toughness grains is investigated in considerable detail through a computational analysis. The dominant factors are the grain size and the effective content of high-toughness grains.