Various numerical techniques such as finite element and boundary element methods are commonly used to analysis engineering problems. These methods encounter mesh-related difficulties in dealing with fracture mechanics problems. To overcome these difficulties, a number of meshless methods have been developed in recent years. In this paper the Element Free Galerkin method based on the linear elastic fracture mechanics is used to model the jointed rock medium under axial loads. The stress intensity factors are calculated on the tip of the joints by using J-integrals. The visibility criterion and a cubic spline weight function are applied to model rock fractures. In addition, the Lagrange multipliers method is employed to enforce the boundary conditions. To verify the computational capability and accuracy of the method, a couple of examples of jointed samples in mode I as well as mixed mode are considered and the stress intensity factors are determined. The obtained results by this technique, in comparison with analytical methods, show a good accuracy and denote that the Element Free Galerkin method can be used as a proper tool in rock fracture mechanics.

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