Classifications of British and Irish vascular plants into floristic elements are reviewed. Only H.C. Watson and J.R. Matthews have attempted to devise a more or less comprehensive classification, based on the British range of the species (Watson) or the European distribution (Matthews). A new classification of 1481 native species is presented, based on their range in the Northern Hemisphere. Species are classified by their occurrence in one or more major biomes (Arctic, Boreal, Temperate, Southern) and their longitudinal distribution (Oceanic, Suboceanic, European, Eurosiberian, Eurasian, Circumpolar). The distribution of species in the floristic elements is illustrated by coincidence maps for the British Isles and Europe. The British and Irish flora is dominated by Boreo-temperate, Temperate and Southern-temperate species, with the Temperate species being the most numerous. Species with continental distributions (i.e. species which are rarer than expected in western Europe) are listed; most of these are in the Boreo-temperate and Temperate elements. The floristic elements are discussed in relation to the life-form spectra, habitat preferences and altitudinal limits of the component species, and analysed in terms ol˜ Ellenberg indicator values for temperature and continentality. The new classification is compared with that of Matthews. An additional 48 species which are endemic to the British Isles are listed. The scope for extending this method of classification to other organisms and for adapting it for use outside the British Isles is discussed.