Abstract: In this paper, the critical failure model is established by renormalization group theory approach, and the relation between the peak strength and the mean strength of the elements is studied. The stress transfer among the elements is defined with the conditional probability method.The critical probability P * is obtained. On the other hand, the whole process of brittle fracture of rock has also been simulated numerically from micro fracture to macro fracture by using the rock failure process analysis(RFPA) code. The peak strengths obtained by the numerical model agree fairly well with those obtained by the renormalization group theory.