Three stochastic rainfall models are evaluated in terms of their ability to reproduce the standard and extreme statistics derived from observed hourly point rainfall data obtained from three different sites in the UK. The models are: a modified version of the Eagleson [Eagleson, P.S., 1972. Dynamics of flood frequency. Water Resources Research 8, 878–898] exponential model (or MEEM), a version of the data-based model of Cameron et al. [Cameron, D.S., Beven, K.J., Tawn, J., Blazkova, S., Naden, P., 1999. Flood frequency estimation for a gauged upland catchment (with uncertainty). Journal of Hydrology 219, 169–187] (or CDFGPDM) and the random parameter Bartlett–Lewis gamma model (or RPBLGM) of Onof and Wheater [Onof, C., Wheater H.S., 1994. Improvements to the modelling of British rainfall using a modified random parameter Bartlett–Lewis rectangular pulse model. Journal of Hydrology 157, 177–195]. The sites are: Elmdon (Birmingham, England), Eskdalemuir (White Esk valley, Scotland), and the Wye (Plynlimon, Wales). For each site, the simulations are conducted on a seasonal (winter and summer) basis, with hourly timestep. For each season, a comparison of the spread of the 1 and 24 h simulated seasonal maximum rainfall totals with those obtained through a statistical analysis of the observed extreme rainfalls is also made. It is shown that the MEEM can effectively reproduce certain observed series standard statistics at each site. It is much poorer in its representation of extreme events, and, for two of the sites, dry periods. The CDFGPDM generally performs well under all the criteria, although it has a tendency to underestimate the observed 1 h seasonal maximum rainfalls for both seasons at Elmdon. The RPBLGM is shown to be reasonable at simulating the standard statistics but is often poorer with respect to the extremes. The implications for flood frequency estimation are highlighted. Possible improvements to each model are considered.