Stress intensity factor is the one of most important parameters in rock fracture mechanics. In practice, this factor is commonly calculated by various numerical techniques such as finite element and boundary element methods. These methods encounter mesh-related difficulties in dealing with fracture mechanics problems. In this paper the Element Free Galerkin method based on the linear elastic fracture mechanics was used to determine tension-mode stress intensity factor in jointed rock medium using stress extrapolation method. The visibility criterion was applied to model the rock fractures. In addition, Lagrange multipliers method was employed to enforce the boundary conditions. To verify the computational capability and accuracy of the method, an example of jointed sample including horizontal joint was considered under tension load and the stress intensity factor was determined and evaluated. The stress extrapolation method with %7 difference in comparison with analytical method has high precision and it also shows good agreement with the displacement extrapolation method based upon finite element method.

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