Geologists create volcanic hazard maps using scientific data to portray potential future geological events; the end users are principally public safety officials. Typical maps use a few simple polygons to outline areas of potential inundation or cover by a few categories of flows based on past frequency and size. Uncertainties in data regarding flow characteristics complicate the construction of accurate hazard maps. Generally, there are inadequate exposures of good sections, poorly known extents of units, and imprecise volumes for deposits. Crisis conditions limit the time available for field and laboratory work. Computer models can simulate possible scenarios, but the volumes, styles of emplacement, and source starting locations are poorly known in many cases. The large uncertainty in initial conditions is seldom taken into account in the construction of hazard maps, and these uncertainties are rarely passed on to the end users of the maps. TITAN2D is a computational model for volcanic block-and-ash flows and rock avalanches of various types and scales, and it forms the core of the TITAN toolkit for volcanic hazard analysis, which can integrate high-performance computing, database management, and visualization to a very sophisticated level. TITAN provides a solution to mapping problems by providing a probabilistic calculation of inundation depth that takes into account many of the critical uncertainties.