In materials with local variations in yield stress, such as functionally graded materials or materials with interfaces or interlayers, the local near-tip crack driving force can become dierent from the nominally applied far-ยฎeld value. The near-tip crack driving force is enhanced, if the yield stress increases in the crack growth direction, and vice versa. This eect is termed as the yield stress gradient eect. A model is developed that allows us to derive analytical expressions to quantify the eect and to evaluate the eective crack driving force for smooth and abrupt variations in yield stress. These expressions can be used to optimize graded materials and interface and interlayer transitions so that the fracture resistance increases. The predictions of the model agree well with the results of previously reported ยฎnite element computations for cracks near bimaterial interfaces. Available experimental observations of the fatigue crack growth normal to interfaces and interlayers can be qualitatively explained. The yield stress gradient eect plays an important role for the fracture behavior in multiphase or composite materials, in functionally graded materials, in materials with special surface treatments like nitrided or case hardened steels, as well as in brazed and welded components.