The crystal plasticity finite element method (CP-FEM) is used to investigate the influence of microstructure on the bending behaviour of the heat treatable aluminium alloy AA7108. The study comprises two materials obtained from the AA7108 aluminium alloy by different thermo-mechanical treatments. The first one is an as-cast and homogenized material consisting of large grains with random texture, while the second one is a rolled and recrystallized material having refined grains with weak deformation texture. The behaviour of the two materials in plane-strain bending is investigated numerically and compared qualitatively to existing experimental data. The crystallographic texture and grain morphology of the materials are explicitly represented in the finite element models. The numerical results display a strong effect of the grain morphology on the bending behaviour, the surface waviness and the development of shear bands. These results are consistent with the experimental observations. The simulations further indicate that crystallographic texture affects the bending behaviour of the rolled and recrystallized material.