Abstract: The plane strain triaxial tests in which the minor active principal stress (also called σ_x) keeps invariable are performed on the compacted loess with different water contents. The influences of σ_x and water content (also called w) on characteristics of the principal stress in plane strain direction (also called σ_y) during loading are studied. Based on the test results, the expressions describing the bilinear relationships between the principal stress in the plane strain direction and that in other directions are proposed. It is verified whether or not σ_y can be predicted by the expressions for the intermediate principal stress based on different strength criteria for compacted loess. The test results show that σ_y is not the intermediate principal stress (also called σ₂) but the minor principal stress (also called σ₃) during the isotropic consolidation and the initial loading stage. The ratio of the principal stress in the plane strain direction to the minor active principal stress (also called σ_y/σ_x) fast increases after the gentle development stage with the increase of the ratio of the major active principal stress to the minor one (also called R), and the relationships between the principal stresses are respectively linear and nonlinear before and after the turning point. The ratio of the major active principal stress to the minor one at the turning point (also called R_z) is larger than that at the critical point where σ_y transforms σ₂ to σ₃ (also called R_c). w and σ_x have obvious influences on R_z but little ones on R_c. The effects of w and σ_x on σ_y/σ_x are little as R is small. The relationships between the principal stress parameter (=2σ_y/(σ_x+σ_z), also called K) and R can be describedas two-stage lines. The one is horizontal and K is constant K_c in the first stage. The other one is inclined upward in the second stage. The slope m and K_c are irrelevant to w and σ_x. The change of σ_y during the loading can be better predicted by the proposed bilinear function. The predicted results are approximately equal to the test ones only at the failure of soil samples, using the expressions for the intermediate