This work presents the existence of buckling mode switching with respect to the radius of concentric rigid ring support. The buckling mode may not be axisymmetric as previously assumed. In general, the plate may buckle in an axisymmetric mode but when the radius of the ring support becomes small, the plate may buckle in an asymmetric mode. The optimum radius of the concentric rigid ring support for maximum buckling load is also determined. Introducing internal rigid ring support, when placed at an optimal position increases the elastic buckling load capacity by 149.39 percent. The numerical results obtained are in good agreement with the previously published data. © 2013 Higher Education Press and Springer-Verlag Berlin Heidelberg.