In order to solve two dynamic propagation problems on mode Ⅲ crack by theory of complex functions,a new mechanical model for dynamic crack propagation,in which the crack is under the conditions of increasing loads Px/t、Pt3/x2 located at the origin of the coordinate of the crack is presented in this paper.The problems are transformed into Riemann-Hilbert problems by the approaches of self-similar functions,and the analytical solutions of stress,displacement and stress intensity factor are attained.With the solutions and superposition theorem,the solutions of discretionary complex problems can be acquired.