Film cooling as an important thermal protection technology is widely used in aviation and ground gas turbine blades. But film cooling holes reduce the strength of blade seriously, which have become a key region of crack nucleation. In this paper, the plastic behaviors of nickel‐base single crystal alloy turbine cooling holes in spanwise injection angles range from 0° to 40° are investigated on basis of crystallographic constitutive theory. The results show that there are both higher stress regions and lower stress regions around multi‐column cooling holes, where suffer stress interference. The maximum Mises stress occurs at the hole in the center column. The places where the maximum resolved shear stresses occurs change with load and spanwise injection angle. The maximum Mises stress around holes with injection angle of 0° is lowest. With the injection angle increases, the maximum Mises stress increases until injection angles up to 30°. In all the slip systems, the resolved shear stress of hexahedral slip system is most sensitive to the changing of spanwise injection angle and load.