The problem of averaging fourth‐rank tensors with texture describing weight functions has been solved for orthotropic physical symmetry and for orthorhombic crystal symmetry. The results are presented in tabular form. The procedure for extending the tabular results to tetragonal, hexagonal, and cubic crystal symmetries is indicated. The solution requires the coefficients of the generalized spherical harmonic expansion of the weight function up to fourth order, and entails only those approximations required to obtain such coefficients from experimental data.