The static and dynamic stability of variably thick orthotropic annular plates subjected to in-plane periodic forces with respect to time is studied. It is assumed that the periodic radial forces with the same period act along both the inner and outer edges of plate. The finite element method is used with a sector element based on the Mindlin plate theory. The wave propagation technique of cyclic symmetry is used in the formulation. The choice of the element enables the analyst to solve the axi-symmetric and asymmetric dynamic stability problem at the same time. Variations in the plate thickness in which it increases or decreases in the radial direction according to the equations h = h(max)(r/r(o))+lambda or h = h(max)(r/r(i))-lambda, respectively are considered. The instability regions for different boundary conditions are determined by Bolotin's method. It is found that the critical buckling load, buckling mode and instability regions are changed by variations in the polar orthotropic material properties.