Elastomeric bearings used as seismic isolators are susceptible to a buckling type of instability similar to that of structural columns. The buckling load and buckling behaviour can be determined from an elastic analysis of the isolator modelled as a continuous composite column with bending and shear flexibility; this analysis cannot be used, however, to assess the post-buckling behaviour or the stability of the isolator at large horizontal displacements. By using a two-spring rigid link model that considers large angles without using linear approximations, it is possible to predict the post-buckling behaviour of an isolator. Using the simple closed form expression, this paper will model three aspects of post-buckled isolator behaviour: the dependence of horizontal stiffness on vertical load, the stability at large horizontal displacements, and the increase of horizontal displacement with respect to axial load and vertical displacement.