Abstract: In this paper the anti-plane moving crackin non-homogeneous elastic materials is studied by an analytical method. First the governing equationsfor homogeneous materials are solved by use of Fourier Cosine integral transform. Then the dualintegral equation for moving crack is establishedaccording to the mixed boundary value conditions. It is shown that the dual integral equation can be reduced to the Fredholm integral equation of thesecond kind. Numerical results presented in thepaper indicate that the non-homogeneity of materialshas an important influence on the dynamic stress intensity factor.