Determination of stress intensity factors is a critical task in fracture mechanics, numerical methods such as the finite element and boundary element methods which have successful applications in various fields of engineering problems, 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 different types of loads. The stress intensity factors are calculated on the tips of the joints by using J-integral or M-integral methods. 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, some examples of jointed samples in mode I and mixed mode are considered and the stress intensity factors are determined. The results obtained from the EFGM models together with J-integral or M-integral, in comparison with analytical and finite element methods, show good accuracy. This study denotes that the element free Galerkin method can be used as a proper tool in rock fracture mechanics.

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