Distance from the sea, proximity of mountains, continentality and elevation are all useful covariates to assist the mapping of extreme rainfalls. Regression models linking these and other variables calculated from a digital terrain model have been built for estimating the median annual maximum rainfall, RMED. This statistic, for rainfall durations between 1 hour and 8 days, is the index variable in the rainfall frequency analysis for the new UK Flood Estimation Handbook. The interpolation of RMED between raingauge sites is most challenging in mountainous regions, which combine the greatest variation in rainfall with the sparsest network of gauges. Sophisticated variables have been developed to account for the influence of topography on extreme rainfall, the geographical orientation of the variables reflecting the prevailing direction of rain-bearing weather systems. The different processes of short and long-duration extreme rainfall are accounted for by separate regression models. The technique of georegression combines estimates from regression models with a map of correction factors interpolated between raingauge locations using the geostatistical method of kriging, to produce final maps of RMED across the UK.