Abstract: By the application of theory of complex functions, the fracture dynamic problems of mode Ⅲ interface cracks subjected to homogenously distributed loads were studied. By the approach of self-similar functions，the dynamic problems can be transformed into Riemann-Hilbert problems, and analytical solutions of the stresse, displacement as well as the dynamic stress intensity factor for moving cracks are obtained by Muskhelishvili’s method. In terms of the relationship between the dislocation distribution function and displacement, the analytical solutions of the dislocation distribution functions are attained and the variational rule of the dislocation distribution function is depicted.