The basic formulas (Reuss′s approximation) for residual stress analysis are given in a revised form. All ODF‐burdened information reduces to five “moment pole figures” simply to, calculate using modern direct algorithms. The corresponding harmonic expressions are also more compact than other formulas known from literature. For texture components described by Standard Gaussian Functions the corresponding expressions can be given in an analytically closed form. The use of the concept of the geometrical mean approximation for calculating elastic constants (avoiding Reuss′s limitations) will be explained in connection with the determination of residual stresses.