A crack in a component grows, if the crack driving force is equal or lager than the crack growth resistance. Since the beginning of elastic-plastic fracture mechanics, a parameter has been searched which describes the crack driving force and is generally applicable. Rice introduced 1968 such a parameter, the J-integral, which is now commonly used in standard fracture mechanics testing. Since the J-integral was derived for nonlinear-elastic materials (i.e. deformation theory of plasticity), its application for real, elastic-plastic materials is connected with certain restrictions. One important restriction is that the J-integral can be used only, if no unloading processes occur in the material. But even if this condition is fulfilled, the J-integral does not describe the crack driving force, but only the intensity of the crack tip field. Simha et al. have recently succeeded in deriving the crack driving force in elastic-plastic materials with incremental theory of plasticity by using the configurational force concept. A new J-integral for elastic-plastic materials, Jep, was found which is able to quantify the crack driving force in elastic-plastic materials. The current thesis deals with the characteristic properties of this new J-integral, Jep, and works out the main differences to the conventional J-integral. In order to do this, numerical studies are conducted to calculate the distribution of the configurational forces in fracture mechanic specimens. The incremental plasticity near-tip and far-field J-integrals are evaluated from the configuration forces and compared to the conventional deformation-plasticity J-integrals. Different parameters are systematically varied, e.g. the stress state, the load, the size of the plastic zone, and the finite element mesh sizes. On the contrary to the conventional J-integral, the new J-integral, Jep, can also be applied for monotonically or cyclically growing cracks. An important topic of the current thesis is to quantify the crack driving force for stationary and growing cracks in elastic-plastic materials with incremental theory of plasticity. Therefore, the path dependency of Jep is examined in great detail for regions very close to the crack tip. However, it is very difficult to separate in this region close to the crack tip numerical inaccuracies from real physical effects. In both cases, Jep decreases if the integration path comes closer to the crack tip; an extrapolation results in . This agrees with an old theoretical work by Rice. While the decrease of Jep for a stationary crack starts only at very small distances to the crack tip, the decrease for a growing crack starts already at much larger distances. The reason is that the singularity of the crack tip field is much weaker for a growing crack than for a stationary crack. These results provide an explanation for the fact, which has been found by detailed experimental observations: Considered at the micro-scale, cracks in engineering materials do not grow continuously, but in discrete steps. Further important points in the current thesis are the determination of the crack growth direction under mixed-mode loading conditions and the calculation of the crack driving force in inhomogeneous elastic-plastic materials with an interface near the crack tip. Detailed case studies show that in these cases Jep and the conventional J-integral deliver nearly identical results, provided that we consider a stationary crack and the conditions of proportional loading are fulfilled.