Most models based on continuum mechanics do not account for inhomogeneities at the micro-scale. This can be achieved by considering a representative volume of material and using (poly)crystal elasto-plastic deformation theory to model the effects of grain morphology and crystallographic orientation. In this way, the relationship between the macroscopic stress state and the stress state at the grain level can be investigated in detail. In addition, this approach enables the determination of the inhomogeneous fields of plastic strain, the identification of regions of localised plasticity (persistent slip bands), grain level shakedown, and the prediction of fatigue crack initiation using energy dissipation at the micro-scale. Elastic anisotropy is known to promote earlier onset of yielding, and to increase the magnitude of intergranular residual stresses. The effect of hardening behaviour of different slip systems on intergranular residual stresses is more subtle, as discussed in the text. The present study focuses on the analysis average intergranular residual strains and stresses that arise within the polycrystal aggregate following the application of single or cyclic external loading. These residual strains can also be evaluated experimentally using diffraction of penetrating radiation, e.g. neutrons or high energy X-rays, allowing comparisons with the model predictions to be made.