The so-called crystallite group (CGM) method, employed for diffraction stress analysis, involves that a possibly complex texture is approximated by a set of one or a few so-called ideal orientations. It has been shown that this approximation can lead to pronounced errors in the determined stress values. The range of applicability of the CGM has been investigated from a theoretical point of view. Numerical simulations of diffraction strain measurements have been performed using orientation distribution functions representing textures of different strength and sharpness. Special emphasis has been put on the fibre-textured case.