Many different fracture criteria have been proposed for the failure prediction of brittle materials using Batdorf's or Evan's weakest link formulation. There are also many reports where efforts have been made to determine which is the most suitable criterion. However, the difference between the predictions is usually small, making it difficult to decide which criterion best describes a given material. A shear-sensitive and a shear-insensitive criterion are critically examined in this paper under various stress states and it is proposed that to distinguish between the criteria the basic material data should be obtained from biaxial tensile tests, e.g. ring-on-ring tests, and that to obtain the greatest difference between the predictions of the different criteria, a torsion test should be performed. Whether predictions are conservative or non-conservative is also discussed. Finally, comparisons are made with a simpler weakest link model which uses the principle of independent actions.