Axial alternating fatigue tests with superimposed static torsional mean stress and shear alternating fatigue tests with superimposed static tensile mean stress are represented. A decrease in the fatigue life of the material was observed with an increase in the shear and static tensile stresses. Marin and modified Crossland methods are analyzed by means of the available experimental data. The two modifications of Sines method are proposed to take into account the static torsional stress effect (Sines+) and different slopes of the S-N curves in tension-compression and torsion tests (Sines++). It is shown that Sines++ model is the most accurate among others.