In our recent work, a new integrated model was proposed to describe the back-stress evolution based on the dislocation substructure and texture. By relating the back-stress to the dislocation density in cell walls and in the cell interior, this model is able to capture the back-stress evolution of ECAP processed pure aluminium. In this paper, the model is used for another FCC material, namely copper. The aim is to check whether this model is able to predict the tension/compression asymmetry (due to the back-stress) of copper. The results show that this is indeed the case and it is also found that the strain rate ratio proposed in our previous work  is a function of the dislocation density ratio.