Summary: Based on the initial boundary value problem of wave-telegraph equations, dynamic problems of the decagonal symmetric two-dimensional quasicrystal material of point group 10mm with a mode II Griffith crack are investigated by using the finite difference method. First, the effects of the loading time, loading location, and specimen size on the crack-tip dynamic stress intensity factor are discussed. Second, the effects of the phonon-phason coupling elastic constant, friction coefficient, and effective mass density on the displacement component of the phason field are discussed, and thus the movement characteristic of the propagation of the phason wave is obtained. The results show that the variation characteristics of the curves corresponding to different related parameters are consistent with the actual physical characteristics. At the same time, when there is a fluctuation characteristic in the phason field, the diffusion characteristic still plays a dominating role.