The plastic anisotropy was studied on aluminium sheets with layers of different purity (A: 5N and B: 2N+) produced by accumulative roll bonding (ARB). Both material layers show a contrasting recrystallization behavior where A and B are discontinuously and continuously recrystallized, respectively. Global textures were measured by neutron diffraction. The mechanical anisotropy was measured by tensile testing after different numbers of ARB cycles. The planar anisotropy decreases with the number of ARB cycles while the normal anisotropy reaches a plateau after 4 cycles. Simulations of the Lankford parameters were carried out with the help of the viscoplastic self-consistent scheme (based on the global texture) and compared with the experimental data. Deviations of the simulated values from those of experiment are discussed with regard to through-thickness texture and material heterogeneities.