Abstract The subject of this paper is the mathematical analysis of the distribution of stress in thin plates of cylindrically aeolotropic material. The plane-stress theory leading to the general solution of this problem under arbitrary boundary conditions is developed in a manner analogous to that used in the corresponding problem involving isotropic materials. The analogy between the plane-stress and plane-strain problems is the same as in the isotropic case, and hence needs no discussion. The following problems are solved: The ring under uniform radial internal and external pressure; the extension of this problem to include the case of the complete disk; the rotating disk; the curved beam bent by end couples; the dislocation problems of the ring; the hydrostatic-stress problem; the force and the couple applied to the vertex of a wedge; and the force applied at a point in the infinite plate. Stresses and displacements are plotted for the first four of the foregoing problems, showing the effect of the degree of anisotropy.