A major challenge in the application of seismic isolation to nuclear structures is the torsional response of base-isolated Nuclear Power plants (NPPs), which amplifies the isolator displacement around the periphery of the isolation system. Additionally, degradation in the mechanical properties of the isolator due to the response associated with extreme ground shaking may also affect the torsional response. This paper presents a comprehensive study on the torsional response of a NPP seismically isolated using lead rubber bearings with a focus on the isolation properties and eccentricity in the isolation system. Nonlinear response history analysis is conducted with different NPP model representations, which are derived from a benchmark NPP model for a range of eccentricities with different time periods and characteristic strengths. It was observed that torsional response in base-isolated NPPs could be controlled by using a flexible isolation system of higher characteristic strength, and it may be important to include the strength degradation in lead rubber isolators to correctly estimate torsional amplification to isolator displacements. The torsional amplification predicted by the nonlinear response history analysis was also compared with the provisions of ASCE 7 for buildings, and recommendations are provided on their suitability for seismically isolated NPPs.