The plastic anisotropy of ultrafine grained aluminium alloys AA1050 and AA6016 produced by accumulative roll bonding (ARB) has been investigated by tensile deformation via the Lankford parameter. The average normal and planar anisotropies slightly increase (from 0.6 to 0.9) and decrease (from 0.6 to −0.7) as a function of ARB cycles, respectively. The global textures measured by neutron diffraction are used to simulate the Lankford and anisotropy parameters of the plates after 0, 2, 4, 6 and 8 ARB cycles with the help of the viscoplastic polycrystal self-consistent model. Simulation results are compared with those from experiment and discussed with regard to texture, strain rate sensitivity, grain shape and slip system activity.