In this paper the Element Free Galerkin Method (EFGM) has been extended to be used in the Elastoplastic stress analysis. The developed method has been examined in planar stress analysis around the tip of a crack and in its opening mode of loading. To do this, at the first step by using the incremental relations of plastic deformation a system of Elastoplastic EFGM equations has been derived. Since the obtained relations are nonlinear, a nonlinear solution technique has been chosen. To examine the validity of this technique, stress fields in two different plates with and without a crack have been calculated and the results have been compared with other similar analytical works in the literature. In doing so the power law work hardening behavior has been employed and the value of J-integral has been used as a base for comparison of the results.

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