Results generated from a detailed long-range transport model, MESOS, simulating dispersal of a large number of hypothetical releases of radionuclides in a variety of meteorological situations over Western Europe, have been used to derive a simpler statistical model, MESOSTAT. This model may be used to generate probability distributions of different levels of contamination at a receptor point 100–1000 km or so from the source (for example, across a frontier in another country) without considering individual release and dispersal scenarios. The model is embodied in a series of equations involving parameters which are determined from such factors as distance between source and receptor, nuclide decay and deposition characteristics, release duration, and geostrophic windrose at the source. Suitable geostrophic windrose data have been derived for source locations covering Western Europe. Special attention has been paid to the relatively improbable extreme values of contamination at the top end of the distribution. In this paper the MESOSTAT model and its development are described, with illustrations of its use and comparison with the original more detailed modelling techniques.