The elastic analysis of a mode Ⅱ Griffith crack penetrating through a decagonal quasi-crystal along the periodicaxis is made within the context of the continuum theory. By using a general solution obtained previously, the problemin the case of uniform shear stress at infinity is solved, and the analytical expressions for the entire stress field disturbedby an inteal crack are derived in an explicit form. The asymptotic fields of the displacement and stress around a cracktip in both phonon and phason fields indicate that the stresses near a crack tip exhibit the square-root singularity. Theformula for evaluating the energy release rate is also given. If imposing that the phason field is absent, the well-knownresults of a mode Ⅱ crack in a conventional material are recovered from the present results.