By application of the theory of complex functions, asymmetrical dynamic propagation problems concerning mode III interface crack were studied. The general representations of analytical solutions are acquired by the approaches of self-similar functions. The problems considered can easily be transformed into Riemann-Hilbert problems and two examples under the action of moving increasing normal force Px/t and increasing loads Pt located at the origin of the coordinates of the crack are given, respectively. After those solutions are used by superposition theorem, the solutions of arbitrarily complex problems can be attained. (C) Koninklijke Brill NV, Leiden, 2010