By the approaches of complex variable functions, two dynamic propagation problems of mode Ⅲ interface crack were researched. The problems considered can be very facilely changed into Riemann-Hilbert problem by means of self-similar functions, and analytical solutions of the stresses, displacements, dynamic stress intensity factors for the edges of mode Ⅲ symmetrical dynamix interface crack subjected to moving increasing loads Pt2/x2 and Px3/t2, respectively, were obtained by the methods of self-similar functions. After those solutions were utilized by superposition theorem, the solutions of arbitrary complex problems can be readily attained.