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In this article, the fractal two-level finite element method, which has mainly been used for static crack problems, is applied to mode III elastodynamic plane crack problems. Using the transformation process in the proposed method, the infinite dimension of the finite element matrices that are assembled for a singular region is made finite in terms of the dynamics stress intensity factors directly and, thus, the computational time and errors can be reduced significantly. The Newmark time integration scheme is then used to obtain the dynamic stress intensity factors for different crack cases. The results from the proposed method are in reasonable agreement with those of classical methods. A parametric study is conducted to investigate the effects of different parameters on the accuracy of the dynamic stress intensity factor. [ABSTRACT FROM AUTHOR]