Abstract: By application of the theory of complex functions, the fracture dynamics problems on the edges of mode Ⅲ moving crack subjected to homogenous loads and moving concentrated variable loads were investagated respectively. Using the approaches of self-similar functions，the problems considered can be transformed into Riemann-Hilbert problems, and analytical solutions of stresses, displacements and dynamic stress intensity factors for moving crack are then obtained by Muskhelishvili’s method. Through the relationship between dislocation distribution functions and displacements, analytical solutions of dislocation distribution functions were attained, and variational rules of dislocation distribution functions were discribed.