Among the limitations of the classical methods for measuring stresses by X-ray diffraction, the existence of stress gradients constitutes a particularly delicate problem. On the theoretical plane, this problem has been tackled by Dölle, Hauk and Cohen. These authors showed that whilst the gradients of the shear stresses σ13 and σ23+ are relatively easy to bring to the fore, as their presence is reflected in an opening out of the curves for 2θ ϕ ψ =f (sin2ψ), those of the direct stresses σ11, σ22 an σ33 are very difficult to detect. In the latter case it is demonstrated that even when the gradients attain very high values, the curves of 2θ ϕ ψ =f (sin2ψ) remain practically linear. This may invite one to apply the classical sin2ψ law, with the result that the stress values so determined do not correspond with the real mechanical state of the surface of the specimen.