A limit point behaviour analysis of a metastructure, composed of two double clamped, initially curved beams, coupled via a rigid truss at their respective centres, is carried out when subjected to a distributed electrostatic load. The analysis is based on a reduced order (RO) model resulting from Galerkin’s decomposition, with symmetric buckling modes taken as the base functions, for either beam. All solutions employed the implicit arc-length “Riks” method to accommodate for winding equilibrium paths, while validation of the said results were carried out against finite differences (FD) direct solutions. In addition, local stability analysis via the energy method, conducted on the primary beam was instrumental in clarifying the role of the various extremum points by characterising which branches are stable, and which are not. The combined analysis has shown that the driving beam, which directly encounters the load, is able to possess bistable as well as tristable properties, provided that the metastructure meets certain geometrical parameters. Several variations of tristability are disclosed in the study. The analysis indicates that a model with at least three degrees of freedom (DOF) is needed to predict such configurations, as well as the various critical thresholds, with reasonable errors of around one percent when compared against FD. In so doing, the model can be used to provide static characterisation of the structure.