Abstract: In this paper, a nonlocal theory of fracture for brittle materials has beenproposed. It contains the nonlocal elastic stress fields of mode-I, II, III Griffith cracks, the asymptotic forms of the stress fields at the neighborhood of the crack tips, and the maximum tensile stress criterion of brittle fracture. As an application of the theory, the fracture criteria of cracks of mode-I, II, III and mixed mode I-II, I-III are given in detail and compared with some experimental data and the theoretical results o...