Film cooling as an important thermal protection technology has been widely used in gas turbine blades. However, due to stress concentration around holes, the cooling holes have become key crack nucleation regions of blades. In this paper, the crystallographic behaviors of cooling holes were analyzed by the crystallographic constitutive model. Film cooling holes in the leading edge was simplified to a flat model. The distributions of resolved shear stress along cooling holes and changes under different hole distances were obtained. The results show that stress interference exits among cooling holes clearly. Higher stress areas appear between the centerlines of the cooling holes in two adjacent columns and the lower stress regions as a diamond-shape occur between two cooling holes in the same columns. All the slip systems of octahedral, dodecahedral and hexahedral will be active. And the maximum resolved shear stresses occur at the angle 0o/20o/30o of cooling hole. With horizontal holes distance increasing, the maximum stress around cooling holes decreases. With the vertical holes distance increasing, the maximum stress around cooling holes increases. In all the slip system, the hexahedral slip systems is the most sensitive to hole distances change