Assuming the weakest link concept. A probalilistic model of fracure in concrete structures has been developed in terms of the critical stress intensity factors. The probabilistic model, wodel, which is expressed in the form of the Weiball distribution, has been compared with arange of experimental results in the literature. The results predicted by the formula are in good agreement with the values reported in the literature for four test secimen geometries-compact tension spectimens, notched three-point bend specinens, wedge splitting spectimens and compact compression specimens. The results presented in the paper have been applied to predict the fracture in large concrete dams and the results compare favourably with observed craking.