We have used a digital model of the topography of Montserrat, a simple mathematical model of gravitational flow and some assumptions of the way in which the next eruption will develop to create a map of the volcanic hazards from Soufriere Hills Volcano. This has been done using an image processing computer to simulate the deposits produced by pyroclastic flows. This technique has the advantages over more traditional cartographic methods of spatial precision, rapid computation of multiple eruption models and the explicit nature of the physical model used. Soufriere Hills Volcano is a small andesitic volcano characterized by a cluster of summit domes and an apron of pyroclastic flow deposits and mudflows upon which several thousand people now live. Most of the flanks were covered by deposits from a series of eruptions from 24000 to 16000 a BP, though there is some evidence that dome growth and small pyroclastic flows have occurred since. The modelling is constrained by field evidence from the deposits of previous eruptions. Although the evidence is not good enough to model individual flow units, the cumulative deposits can be used. From the eruption deposit models we have created a new type of map specifically for emergency planning. This sequential hazard zone map attempts to portray the regions that would be at hazard from pyroclastic flows during successive stages from the start of an eruption whose energy release was increasing with time.