This thesis reviews current methodologies for conducting seismic Probabilistic Risk Assessment (PSA) for nuclear power plants, focussing on methods allowing for uncer- tainties in PSA input data. The techniques used to characterise earthquake ground motion and component failure probabilities (fragilities) and their uncertainties are described, and the methods used to include this data in PSA models are explained. The thesis shows that use of a classical Monte Carlo technique for including data uncertainties in seismic PSA involves statistical combination of results from multiple executions of the PSA model with different input data values. The chief difficulty in the Monte Carlo method arises because the conditional probability of failure of plant components depends on the ground motion associated with the seismic event which is itself subject to significant uncertainties, particularly for rare seismic events. To overcome some of these difficulties, this thesis develops a simplified Monte Carlo method for including uncertainties in seismic PSA. The new method uses properties of log-normal distributions to combine uncertainties in seismic ground motion and component fragilities, avoiding the multiple Monte Carlo calculations of the ’ex- act’ Monte Carlo method. Errors due to dependencies introduced by following the simplified approach are estimated and judged to be acceptable for typical PSAs. The new method is applied to a simplified seismic PSA model previously developed for a PWR type reactor. Results obtained with the simplified method are compared with those obtained with the ’exact’ Monte Carlo approach and with those obtained when data uncertainties are ignored completely. The comparison confirms that the approximate Monte Carlo method gives estimates of core melt frequency that are comparable to those found the ’exact’ Monte Carlo method. However, the mean core melt frequency estimated using both Monte Carlo methods is about four times higher than that obtained ignoring uncertainties, showing the importance of taking account of data uncertainties when carrying out seismic PSAs for nuclear power plants.