This paper provides a simple, albeit accurate, criterion for prediction of the rupture loads of brittle, or quasi-brittle, U-notched samples, where linear elastic fracture mechanics is not applicable because blunted notches do not exhibit stress singularities. Good agreement is found between numerical predictions and experimental results. The results of fracture tests from 18 different ceramic materials and a polymer (at −60 • C) are summarized and are used as a reference for checking the fracture criterion. Seven fracture criteria are reviewed and it is shown that all can be recast into the proposed criterion.