Assessments of pyroclastic flow (PF) hazards are commonly based on mapping of PF and surge deposits and estimations of inundation limits, and/or computer models of varying degrees of sophistication. In volcanic crises a PF hazard map may be sorely needed, but limited time, exposures, or safety aspects may preclude fieldwork, and insufficient time or baseline data may be available for reliable dynamic simulations. We have developed a statistically constrained simulation model for block-and-ash type PFs to estimate potential areas of inundation by adapting methodology from Iverson et al. (Geol Soc America Bull 110:972-984, (1998) for lahars. The predictive equations for block-and-ash PFs are calibrated with data from several volcanoes and given by A = (0.05 to 0.1) V^2/3, B = (35 to 40) V^2/3, where A is cross-sectional area of inundation, B is planimetric area and V is deposit volume. The proportionality coefficients were obtained from regression analyses and comparison of simulations to mapped deposits. The method embeds the predictive equations in a GIS program coupled with DEM topography, using the LAHARZ program of Schilling (1998). Although the method is objective and reproducible, any PF hazard zone so computed should be considered as an approximate guide only, due to uncertainties on the coefficients applicable to individual PFs, the authenticity of DEM details, and the volume of future collapses. The statistical uncertainty of the predictive equations, which imply a factor of two or more in predicting A or B for a specified V, is superposed on the uncertainty of forecasting V for the next PF to descend a particular valley. Multiple inundation zones, produced by simulations using a selected range of volumes, partly accommodate these uncertainties. The resulting maps show graphically that PF inundation potentials are highest nearest volcano sources and along valley thalwegs, and diminish with distance from source and lateral distance from thalweg. The model does not explicitly consider dynamic behavior, which can be important. Ash-cloud surge impact limits must be extended beyond PF hazard zones and we provide several approaches to do this. The method has been used to supply PF and surge hazard maps in two crises: Merapi 2006; and Montserrat 2006-2007. Springer-Verlag 2008.