In this paper,we investigate the well-known problem of a finite width strip with a single edge crack,which is useful in basic engineering and material science.By extending the configuration to a two-dimensional decagonal quasicrystal, we obtain the analytic solutions of modesⅠandⅡusing the transcendental function conformal mapping technique.Our calculation results provide an accurate estimate of the stress intensity factors K_Ⅰand K_Ⅱ,which can be expressed in a quite simple form and are essential in the fracture theory of quasicrystals.Meanwhile,we suggest a generalized cohesive force model for the configuration to a two-dimensional decagonal quasicrystal.The results may provide theoretical guidance for the fracture theory of two-dimensional decagonal quasicrystals. In this paper, we investigate the well-known problem of a finite width strip with a single edge crack, which is useful in basic engineering and material science.By extending the configuration to a two-dimensional decagonal quasicrystal, we obtain the analytic solutions of modes I and II using the transcendental function conformal mapping technique. Our calculation results provide an accurate estimate of the stress intensity factors K_I and K_II, which can be expressed in a quite simple form and are essential in the fracture theory of quasicrystals. Mianwhile, we suggest a generalized cohesive force model for the configuration to a two-dimensional decagonal quasicrystal. The results may provide theoretical guidance for the fracture theory of two-dimensional decagonal quasicrystals.