Abstract: The structure of loess consisting of horizontally deposited planes and vertically extended micro-fractures makes the anisotropic strength behavior of loess remarkable. Through triaxial tests, three principal stresses are alternatively loaded on loess specimens along the direction of vertical micro-fracture and two orthogonal directions in horizontally deposited plane, whose stress conditions are respectively corresponding to three sectors in the octahedral plane of geometric space. The experimental results reveal the laws of shear stress-strain and strength under different stress paths that the shear stress when the major principal stress is applied in the direction of vertical fracture is commonly larger than one during the major principal stress is loaded in the two orthogonal directions; the larger intermediate principal stress can induce more significant anisotropic structure of loess; the yield loci in the octahedral plane for cross-isotropic or cross-anisotropic loess appear to be elliptical, circular and triangular with curved edges changing with the increase of spherical stress, and elliptical yield locus can be approximatively expressed by the strength criterion of AC-SMP or AE-SMP.