A non-linear system of partial differential equations with symmetries often exhibit bifurcations. In this research work, the symmetry based reduction is applied to the instabilities of a circular von-Kármán plate with stiffened boundary, where the mismatch strain between the edge and the rest of the plate is treated as the bifurcation parameter. This problem is qualitatively motivated by applications in engineering and sciences, for example, composite structures, biological systems, etc. As part of the analysis, the nonlinear differential operator on a suitable Banach space is formulated using variational approach; then the null space of the linearized operator is constructed relative to the trivial (homogeneous deformation) solution. After identifying the symmetry and its relevant subgroups for the operator, the reduced problem is formulated. The critical parameter values for a potential bifurcation in the reduced problems are determined. It has been found that the critical modes occur in two distinct patterns. In the first pattern, the interior of the plate undergoes dominant deformation. This pattern has been found with infinitely many critical values for the same symmetry subgroup. The second pattern exhibits a dominant deformation at edge. This pattern has been found for single critical value for each symmetry subgroup. The critical parameter values are expected to be bifurcation points due to the physical nature of this problem. The semi-analytically obtained results are compared with those found using a developed symmetry based numerical scheme. The postbuckling analysis is carried out using symmetry based Lyapunov–Schmidt reduction\cite{healey881} and the results are verified using finite element method for few critical parameters. Parameter study of a few select solution branches is carried out to highlight features of the problem. The research to be presented in this talk is part of the ongoing PhD thesis of the first author.