When comparing the results of residual stress measurements from a mechanical deflection method and an X-ray stress measurement, often a difference is found between the two methods. A possible reason for this difference is the fundamental difference in elastic behaviour from the material on the surface as in the bulk of the material. Two extreme models are presented and a mixed model is proposed to describe the elastic behaviour of a single crystal in a polycrystalline material. The true elastic behaviour of textured and isotrope materials is compared with the model. This is done by comparing the elastic constants and the shape of the d-sin2 Ψ curves.