Abstract Next to the shape of a growing crack, it is of importance to predict the initiation of new cracks, especially in structures with stress concentrations due to e.g. holes or notches. In the past, different criteria for crack initiation have been discussed. Furthermore, cracks growing in the vicinity of such stress concentrations in general are deflected and therefore complex crack paths arise. The prediction of crack initiation and the shape of crack paths becomes even more complicated if a material exhibits anisotropic constitutive properties or fracture toughnesses. In this paper, a unified approach of material forces for the prediction of the initiation and growth of a crack is presented. The material or configurational forces as crack driving quantity are strongly related to path-independent integrals, e.g. the Jk-integral. A novel methodology is presented for accurately calculating material forces at cracks employing local numerical data. Material tractions at a round U-notch are investigated and related to crack initiation.