The effect of different continuous material parameter functions in the non-homogeneous region on the eigen-functions of crack tip fields is studied by means of the semi-analytical numerical method based on the wedge shaped non-homogeneous sector model. The cases of the different opening angles of the non-homogeneous region, the different dissimilar material ratios, the different configurations, etc. are analyzed systematically. The result shows that the effect becomes smaller as the opening angle of the wedge shaped non-homogeneous sector becomes smaller. The valuable conclusion is drawn that the differences among the eigen-functions corresponding to the cases can be neglected as long as the opening angle is small enough for the engineering application, which facilitates the engineering application of the non-homogeneous region model.