Abstract: The strength laws of natural soils are complex because of their anisotropic and structural properties, and stress anisotropy and damage of structures under loading. By analyzing the shear failure planes or spatially mobilized planes of the Mohr-Coulomb criterion, Drucker-Prager criterion and Matsuoka-Nakai strength criterion, two kinds of spatially mobilized planes, static spatially mobilized plane with unchanging normal direction and dynamic spatially mobilized plane with changing normal direction, are proposed respectively by changing the characteristics of normal direction on the spatially mobilized plane. According to the Mohr-Coulomb failure plane and Matsuoka-Nakai’s spatially mobilized plane, the static axial symmetrical compression spatially mobilized plane and axial extension spatially mobilized plane are obtained respectively under axial symmetrical compression and axial extension stress states. Assuming the linear relation between shear stress and normal stress on the spatially mobilized plane of soil element, the new isotropic and anisotropic strength criteria are established based on the stress conditions of two kinds of static spatially mobilized planes, which are determined respectively by the axial symmetrical compression and axial symmetrical extension stress states. For the intact loess with micro-structural characteristics including vertical crack and transversely isotropic body, the anisotropic strength is revealed by the true triaxial experiments on intact loess, in which the maximum principal stress, intermediate principal stress or minor principal stress act on the vertical direction of loess sample. Considering the relationship between the Cartesian coordinates corresponding to vertical crack of loess and rotation of the maximum, intermediate and minor principal stress axes, the spatial strength surface in the principal stress space being the same as that in the Cartesian coordinates. At the same time, the rationality of the above strength criteria is validated by the true axial test results of intact loess with vertical crack structure. The new strength criteria are analyzed by the geometrical characteristics of strength surfaces in the