Residual stresses in a polycrystalline material have been determined experimentally at different length scales using three different techniques, with the aim of obtaining quantitative values. The polycrystalline material used is the electrolyte of solid oxide fuel cells, made of yttria-stabilized zirconia and submitted to a high biaxial compression stress state. Macroscopic measurements were performed using traditional X-ray diffraction with the sin2? method. Residual stresses within the grains were determined by the X-ray microdiffraction technique using synchrotron radiation. The variation in the strain within each grain was analysed by high-resolution electron backscatter diffraction. The results are self-consistent and give further information on the relation between strain/stress values and grain orientation, and on intragranular strain variations. These results are very important for the validation of mechanical microscopic constitutive equations