It is well-known that the present mixed mode brittle fracture criteria are all the opening mode fracture criterion. We consider that mixed mode brittle fracture of sliding mode fracture exists too. Hence we propose three criteria of mixed mode brittle fracture of sliding mode fracture;: the radial shearing stress criterion, the maximum shearing stress criterion and the distortional strain-energy-density criterion. Thus, we can overall explain the phenomena of brittle fracture in the structural elements with cracks.