Fibre-reinforced elastomeric isolator (FREI) in an un-bonded application is an improved device for seismic mitigation of low-rise buildings. It is expected to reduce the cost, weight and provide easier installation in comparison to the conventional elastomeric isolator, which consists of elastomeric layers interleaved with steel plate as reinforcement. The horizontal response of un-bonded isolator is nonlinear due to rollover deformation and the horizontal stiffness is a function of both vertical load and horizontal displacement. Most previous studies have been focused to develop the model for predicting stability of the bonded conventional elastomeric isolators with low shape factors. In the present study, predicting stability of a prototype un-bonded FREI is presented based on the dynamic response utilizing finite element (FE) analysis. A prototype isolator is investigated under the variation of vertical loads and cyclic horizontal displacement to evaluate the performance and the effect of the vertical load on the behaviour of the isolator. FE analysis result shows that the critical load capacity of the isolator is significantly higher than the design vertical load, and the effective horizontal stiffness decreases with the increase in the vertical loads. Furthermore, the horizontal response of the isolator is also conducted under the design vertical load and increasing horizontal displacement up to 2.00t_r to observe the rollout instability.