A modified random pulse Bartlett–Lewis stochastic rainfall model is used for extreme rainfall simulation. The model features the use of a generalised pareto distribution (GPD) to represent the depths of high intensity raincells. A point rainfall record, obtained from a UK site is used to test the model. Parameter estimation is carried out using a two-stage approach based on the generalised likelihood uncertainty estimation (GLUE) methodology. This procedure acknowledges the limited sample of the extreme rainfall data in the observed record in conditioning individual realisations of the random storm model. The extreme rainfall simulations produced using the model are shown to compare favourably with the site's observed series seasonal maxima. A comparison of the modelled extreme rainfall amounts, with those obtained from a direct statistical analysis of the data, is also conducted.