In this work, we attempt to simulate residual stresses and springback of a deformed metal part based on a micro-macro modelling of the elastic and plastic strains. Samples cut out of an aluminium plate, under different angles relative to the rolling direction, have been bent around a die. The springback angle has been measured in order to estimate the accuracy of numerical simulations. To start, a finite element code with an isotropic material law is applied, showing that most plate sections deform under the action of a pure bending moment (i.e. shear forces are negligible). Using this result, the effect of texture on the elastic springback is simulated with a polycrystalline elastic-plastic theory. Here, the stress state is computed for different layers across the plate under the hypothesis of a homogeneously deforming polycrystal. Unloading is simulated subsequently by reducing the bending moment down to zero. The predictions are compared to the experimental results and the stress profile across the plate thickness is analysed during loading and after unloading. In the discussion, attention is paid to the effects of anisotropy and the relevance of implementing polycrystalline elasto-plasticity into finite element modelling.