Abstract: The geotechnical materials in nature are affected by the natural sedimentation and often have significant cross-isotropic characteristics. The difference in strength and deformation of structural units of soil in different directions is the main issue that should be considered when affecting the design and construction of large-scale civil and hydraulic projects. The research on the cross isotropy of geotechnical materials is of great scientific significance to the safety and stability of actual engineering structures. Based on the study on the relationship among the strength variation of octahedral principal stress space domain, the spatial mobilized plane and the stress state, a comprehensive parameter reflecting the stress conditions and material properties is defined. By analyzing the relationship among this parameter, the failure stress and the stress state, the physical meaning of the parameter is clarified, and based on the space plane strength theory, the sliding failure of the three principal stress planes is considered. It is assumed that the space on the ratio of the shear stress to the normal stress is constant, and a cross-isotropic failure criterion is established considering that the spatial sliding surface of geomaterials changes with the stress conditions of the spatial stress domain. Compared with the experimental results, it is shown that the cross-isotropic failure criterion based on the spatial mobilized plane variation can better reflect the strength characteristics of the materials, and it is particularly applicable to the strength prediction of the stress region when the principal stress axis deflects.