This article presents the exact elastic buckling of annular plates with elastically restrained edges against rotation and translation at inner and outer periphery. The classical plate theory is used to derive the governing differential equation for annular plate with elastically restrained edge support system. The buckling mode may not be axisymmetric as previously assumed. In certain cases, an asymmetric mode would yield a lower (critical) buckling load. This is due to switching of mode. This work presents the critical buckling load parameters for axisymmetric and asymmetric buckling modes. Extensive data is tabulated so that pertinent conclusions can be arrived at on the influence of rotational and translational restraints, Poisson's ratio and other boundary conditions on the buckling of uniform isotropic annular plates. The numerical results obtained are in good agreement with the previously published data. In this article, the characteristic equations are exact; therefore, the results can be calculated to any accuracy. Copyright © Taylor & Francis Group, LLC.