Research Abstract 
Stress intensity factors (abr. SIF) K are very important parameters in fracture mechanics which are characterized as the coefficient of the solution (displacement) of linear elastic system. SIF K depend on the shape of materials Omega, the shape of crack Sigma and the loads F,that is, K is the functional of {Omega, Sigma, F}. There are many researches on SIF by analyitical calculation, numerical results and experiments in individual cases, but systematic researches are few. In this research, we derive the formula which express the shape sensitivity analysis of SIF with respect to the shape of materials Omega. This formula is derived using the expression of SIF by dual singular solution technique and GJintegral techique proposed by the author, which is given the Rintegral expressin dR (u, Z) + (boundary integral). Here u is the solution, Z is the regular term of the dual singular solution, dR is the first variation of Rintegral (area integral) of GJintegral. If the solutions u and Z are regular on the perturbation, then we can change Rexpression to Pexpression (lineintegral) by the fundamental property of GJintegral that clarify the analytical property of the shape sensitivity. For the numerical analysis, we want to use the extension of the language for finite element method created by Prof. Pironneau Olivier et al. in France. Already we added the functions ; the area integral, line integtal, smooth cutoff functions and its partial derivatives.
