The present work is concerned with the modelling of damage initiation and growth in Al-Zn-Mg alloys, and also with an estimation of the ductility in uniaxial tension. An elastoplastic self-consistent model is developed accounting for crystallographic texture and grain shape effects, which also integrates the voids formed by the damage process. The damage evolution is followed within this framework, allowing the prediction of the macroscopic mechanical behavior, and particularly the stress-strain curves for different tensile directions. A bifurcation analysis adapted for this anisotropic compressible case was developed and used to estimate the ductility. Effects of texture, grain shape and critical parameters for damage nucleation are investigated on a theoretical basis. The observed yield stress and fracture strain vs tensile angle profiles observed experimentally can be predicted for certain cases.