The stress field of an interfacial crack in non-homogeneous materials is computed using the semi-analytical method of arbitrary lines (MAL). Then, the eigen-functions of stress, strain and displacement, i.e. the angular distribution functions near a crack tip, are analyzed based on our wedge-shape non-homogeneous model. Finally, the growing direction of the interfacial crack is determined according to the relevant maximum normal stress criterion accurately. Therefore, the effective approach is provided for solving the complicated crack growing directions of an interfacial crack in non-homogeneous materials.