Abstract: Dynamic propagation of asymmetrical mode III interfacecrack were investigated with the theory of complex functions. It can betranslated into a Riemann-Hilbert problem by means of self-similarfunctions, and the universal representations of analytical solution wereobtained when there is Pt / x or Px^3 / t^2 load at the origin of thecrack coordinates. The closed-form solutions can also be simply obtainedwith Muskhelishvili's theory.