The anisotropic mechanical response of f.c.c. metals deformed up to large strains at low homologous temperatures is controlled by interfaces, namely by fragment and grain boundaries. The proposed model starts from initial grain orientations and the corresponding slip rates as predicted by a full constraints (FC) Taylor code. It describes the cell structure development on the microscopic scale and the fragment structure development on the mesoscopic scale in terms of evolution equations for dislocation densities in the twelve f.c.c. slip systems and for disclination densities in six fragment boundary families, respectively. The redundant dislocation densities (or: the cell walls) and the immobile disclination densities and strengths (or: the fragment boundary triple junctions) are connected to critical resolved shear stress (CRSS) contributions. Thus, substructure and texture evolution as well as the resulting macroscopic mechanical behaviour are coupled to each other. Results for several initial grain orientations are presented and compared to experimental observations.