By the theory of complex functions, the dynamic propagation problem on Dugdale model of mode Ⅲ interface crack for nonlinear characters of materials was studied. The general expressions of analytical solutions are obtained by the methods of self-similar functions. The problems dealt with can be easily transformed into RiemannHilbert problems and their closed solutions are attained rather simply by this approach.After those solutions were utilized by superposition theorem, the solutions of arbitrarily complex problems could be obtained.