Abstract: The structure of loess consisting of vertically extended cracks and horizontally deposited planes makes the cross-anisotropic strength behavior. In view of this, by using consolidated drained true triaxial tests, three principal stresses are alternatively loaded along the vertical direction. According to the geometric symmetry relation of the vertical principal stress axis in the stress state in the eight planes, the strength variation laws of the meridional plane in the three spatial domains with vertical and arbitrary horizontal forces and the variation laws of cohesion and internal friction angle with the ratio of the principal stress are analyzed, and the failure surface of the loom with transversely isotropic structure on the octahedral plane is obtained. Under the condition that the two principal stress axes are orthogonal to the vertical principal stress axis without orthogonal rotation, based on the theory of the principal stress space rotation proposed by Lade, the existing isotropic strength expression is improved and developed, and a new strength criterion for the rotation of principal stress axis in cross-anisotropic loess is proposed. The essential effectiveness of the new criterion is confirmed by the results of experimental facts.