Elastomeric and lead-rubber seismic isolation bearings have been widely used in the United States and around the world for the past thirty years. During earthquake ground shaking, these bearings will be subjected to vertical compressive loads due to gravity plus seismic forces, accompanied by simultaneous large lateral displacements. The design of isolation systems composed of these bearings, therefore, requires stability of the isolation system and individual bearings at the maximum displacement be demonstrated. The current codified procedure for assessing the stability of individual bearings uses a ratio of areas, referred to as the reduced area method, to determine the critical load capacity of the bearings at a given lateral displacement. This critical load capacity must be greater than a combination of vertical forces imposed on the bearing for stability to be demonstrated. While the reduced area method provides a simple means for estimating the critical load of a bearing at a given lateral displacement, it lacks a rigorous theoretical basis and has been shown to provide inconsistent predictions by comparison to data obtained from quasi-static testing of individual bearings. Dynamic stability testing of two isolation systems composed of four elastomeric bearings was performed at the University at Buffalo using the UB-NEES earthquake simulators to gain an improved understanding of the stability behavior of the individual bearings and global system under representative earthquake ground shaking. This paper presents: (1) a summary of the dynamic stability tests; (2) sample experimental results; and (3) a discussion of the implications for the assessment of stability in design. The new experimental results presented in this paper demonstrate: (1) instability in individual bearings does not necessarily lead to global instability; (2) the state of the global isolation system should be used to assess stability to economize the design; and (3) the reduced area method is not able to accurately predict the global stability of the isolation system.