Seismic isolation is an effective measure for mitigating the earthquake hazard on important structures such as hospitals, bridges, and nuclear power plants. Seismically isolated structures should remain essentially elastic for the design earthquake, experiencing minimal or no damage. Steel-reinforced elastomeric bearings are seismic isolation devices that are used extensively for the protection of bridges. Because isolators are critical elements of an isolated bridge, they should experience limited, if any, damage during earthquake shaking that exceeds the design level. Damage associated with yielding of the reinforcing steel shims in seismic isolation elastomeric bearings has received limited attention in the literature. In this context, this paper investigates the effect of the steel reinforcement characteristics on the behaviour of rubber bearings under combined axial load, shear displacement, and rotation. The potential of damage in the steel shims under design shear strains is investigated by utilising a damage factor, Ω, with emphasis being placed on various steel shim thickness values. The investigation is carried out using advanced finite element analysis simulations in ABAQUS/CAE. The research showed that local stresses are developed within the steel shims that exceed the yielding limit of the steel reinforcements. These stresses cause permanent deflections and local damage that alters the properties of the isolators.