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An efficient tool is presented to predict the behavior of cracks in all kinds of multi-phase orcomposite materials where the material properties exhibit a spatial variation. Based on thematerial (or configurational) force approach, this tool accurately computes the crack drivingforce and the crack growth direction in inhomogeneous elastic or elastic-plastic materials.The local crack driving force vector Jtip is evaluated as a vector sum of the far-field Jintegralvector Jfar and the so-called material inhomogeneity term vector, Cinh. The latter termquantifies the crack tip shielding or anti-shielding effect of the material inhomogeneities. Forexample, an increase of the elastic modulus or the yield stress in the direction of crackextension induces a negative material inhomogeneity term which provides a shielding effect[1,2]. The components of the vector Jfar are evaluated using a conventional J-integralevaluation procedure by assuming virtual crack extensions in two different directions, e.g.,along and perpendicular to the direction of a pre-existing crack. The components of Cinh areevaluated by a post-processing procedure after the conventional finite element stress analysis[1,2]. In accordance with the criterion of maximum energy dissipation [3,4], the crackextension follows the direction of the local crack driving force vector Jtip.The procedure allows us to take into account smooth material property variations as theyoccur, e.g., in functionally gradient materials, as well as jumps of the material properties atsharp interfaces between two different components. The effect of residual stresses can be alsoaccounted for. To demonstrate the ability of the procedure, it is applied to specimenscontaining sharp bimaterial interfaces with different orientations with respect to the crack.Elastic and elastic-plastic bimaterials are considered, as well as a variation of only theYoung's modulus, of only the yield stress, and the simultaneous variation of both materialparameters. The results of the model are compared to the results of different other criteriaknown from literature, such as the maximum tangential stress criterion or the minimum strainenergy density criterion. It is shown that in some cases large discrepancies between thedifferent criteria appear.