Abstract: Considering the original anisotropic properties of the geomaterials in the process of natural formation, it is simplified as a kind of cross-anisotropy material. Based on a strength criterion, according to the spatial location relationship of depositional plane(DP) and the effective spatial mobilized plane(ESMP) in physical space, the angle of above two planes is regarded as the primary influential factor to measure the strength degree of geomaterial anisotropy. According the concept of ESMP, when the angle between DP and ESMP is larger, the frictional behavior capacity can be fully employed. The stress ratio strength is larger and vice in contrary. Based on the above thought, the stress ratio strength formula for cross-anisotropy material is established. The formula can be employed to revise a strength criterion and a strength criterion considering cross-anisotropy is obtained. The transformation idea of a criterion for transversely isotropic materials formula to isotropic Von-Mises criterion formula is adopted. Based on cross-anisotropy a strength criterion, the transformed stress equation is derived and it can be employed to transform the cross-anisotropy stress space to isotropic stress space. By using the proposed transformed stress(TS) method, it is convenient to convert the traditional two-dimensional constitutive models established on the basis of Von-Mises criterion to the three-dimensional models considering cross-anisotropy. By comparison of the prediction and test results of strength and stress-strain relationship for geomaterials under triaxial loading condition, the validity and applicability of proposed criterion and TS method is demonstrated.