A full closed-form analysis, based upon the Filonenko-Borodich small displacement technique, for the stress distribution within rotating, constant thickness, annular, anisotropic discs, is given. The solutions obtained are much more general than those arising from the use of the very specific orthotropic condition, which is misleadingly described as anisotropic by many authors. However, in order to test the validity of this technique stress distributions for the orthotropic case (Vθ/Eθ = Vr/Er) have been computed with its aid. These results are compared favourably with those obtained by previous authors, and highlight the influence of the radius ratio, anisotropic constant, and Poisson's ratio upon the stress distribution.