In order to examine the distributions stress and displacement with the internal dissymmetrical crack, an asymmetrical dynamic crack design is presented for bridging fiber pull-out in unidirectional composite materials. The crack extension should also appear in the format of self-similarity because fiber failure is ascertained by the maximum tensile stress. The formulation involves the development of a Riemann-Hilbert problem. Analytical solutions under the conditions of an increasing motive force Pt3 / x3 , Px3 / t 2 are closed for an asymmetrical dynamic crack with bridging fiber pull-out, respectively.