The critical angular speed of rotating polar orthotropic circular plates whose outer boundary is constrained from deforming radially is obtained as a function of ply orientation angle. Because the expressions obtained for radial compressive stresses formed due to centrifugal forces were complicated, attaining a closed-form solution of the governing differential equation was not possible. Galerkin formulation of the finite element method has been resorted to, and the results are presented for a full plate and for a plate fixed at its center to a rigid shaft. Increasing the angle of ply orientation up to a certain value decreased the critical speed. In the case of a concentric shaft, increasing the shaft radius increased the critical speed, contributing to the stability of the plate.