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• Under reversal stressing dislocations are pushed back and forth creating microdamage. • It is the Bauschinger (Bau) effect, which declines heavily the fatigue life. • The equations of fatigue for reversal stressing are derived using the Bau-quant of damage energy. • This Bau-quant is found 4–9 times greater then the pulse-quant of one-sign stressing. • The possible explanation of different changes of the yielding limit under tension vs compression is given. The problem of reversal fatigue is solved by introducing a Bau-quant of damage energy , which is incorporated into the constitutive equations of fatigue life for symmetric/asymmetric stressing under constant maximum stress amplitude. This is a continuation of the model of one-sign stressing. The Bauschinger (Bau) effect is the origin of the heavy decline in the fatigue life of the metals, due to intensive grinding of the dislocations and their fast saturation when pushed back and forth during hundreds of thousands of transition at the zero stress point. The constitutive model of fatigue under reversal stressing is based on the balance of passive elastic energy (predicted by the model) with the energy spent on damage, (calculated, using Bau-quant). The Bau-effect reflects its own mechanism of depletion of the passive elastic energy, without mediators as pliancy. This model allows calculation of the Bau-quant value from data and, as found from the published experiments, it is 4-9 times larger then the pulse-quant. This model embraces a wide set of parameters of the metal, the pulses, the Bau-quant, and the stressing and is sensitive to their changes. [ABSTRACT FROM AUTHOR]