A stochastic model, named DOWNFLOW, is presented to forecast possible lava flow paths with the aim of hazard assessment and mitigation. The model relies on the fact that lava flow emplacement is, in many cases, controlled by topography. The potential inundation area of the flow is determined by considering a number of steepest paths over stochastic perturbations of the original topography. Since the code requires very short computational time and few input data the model proved to be a very useful tool to obtain real-time predictions during the initial phase of an eruption. The necessary topographic information can be obtained by photogrammetry, radar altimetry, or laser scanning techniques. DOWNFLOW has been successfully applied to a number of flows, including the September 2004 lava flow, where updated topographies were available.