An earlier paper demonstrated the effectiveness of calculating the ultimate load for a plane weakened by a lune-shaped hole, using Novozhilov's criterion in the case of a uniaxial tensile stress at infinity. In this paper, we examine the problem of fracture of regions with angular concentrators under conditions of a complex stressed state. In considering this case in the asymptotic representation of the stresses in the neighborhood of the corner points, for aperture angles gamma greater than 2. 25, we consider two singular terms, one of which is generated by the tensile stress, the other by the shear. Using the example of an elastic plane weakened by a lune-shaped hole, with a specified stress field at infinity that is made up of uniaxial extension and pure shear, we systematically analyze the possibility of employing Novozhilov's criterion for determining the breaking loads for bodies containing angular notches.