Residual stress measurements on strongly textured materials using the standard sin2ψ evaluation show significant non-linearities. According to EN 15305 there is currently no existing solution for this problem. A method is presented that solves this problem. It is based on two tools. (i) The use of a one-dimensional detector having a large capture angle that yields the full diffraction profiles at each point of the pole figures. Therefore, some hundreds of d-values can be used for the stress calculation. (ii) Data evaluation with the recently developed generalized sin2ψ method. This has the advantage of being based on a flawless theory (Hooke's law in the special form of Dölle–Hauk's equation) and being able to handle any distribution of measurement directions and any number of measured data. The method was successfully tried out at a sheet of brass with significant texture.