Abstarct: In this thesis, the extended finite element method is used to model a finite domain which contains a crack that the surface is subjected to a concentration shock. The dynamic coupled elastic diffusion equations are considered. The Non-iterative version of the newmark scheme is used to solve semi discrete governing equations. The interaction integral is used to extract SIFs. In this research, the effect of relaxation time on the concentration distribution and SIFs under concentration shock are investigated. Also, the time variation of SIFs are investigated in time interval at which the waves pass through the crack tip. The effect of integral domain, mesh sizes and time steps on the time variation of SIFs are investigated. Furthermore, variation of concentration near the tip of an inclined crack due to the reflection of the concentration wave from its surface and consequently local deviation in concentration and displacement fields are discussed in detail.