An analytical study of the natural frequencies and mode shapes of anisotropic thin plates is presented. The plates are considered to be constructed from an orthotropic material such that the principal elastic axes of the materials are not parallel to the plate edges. By use of Galerkin's method, the change in natural frequencies and mode shapes are investigated as the material elastic axes are rotated with respect to the natural geometric coordinates. Three sets of edge conditions are considered: (1) all edges simply supported; (2) one pair of opposite edges fixed with the other pair free; and (3) one edge fixed with remaining edges free. The results of this investigation show that the plate mode shapes are strongly affected by the orientation of the elastic axes and that they cannot be predicted on the basis of conventional isotropic‐ or orthotropic‐plate analysis.