Previous models of degassing, cooling and compaction of rhyolitic ash flow deposits are combined in a single computational model that runs on a personal computer. The model applies to a broader range of initial and boundary conditions than Riehle's earlier model, which did not integrate heat and mass flux with compaction and which for compound units was limited to two deposits. Model temperatures and gas pressures compare well with simple measured examples. The results indicate that degassing of volatiles present at deposition occurs within days to a few weeks. Compaction occurs for weeks to two to three years unless halted by devitrification; near-emplacement temperatures can persist for tens of years in the interiors of thick deposits. Even modest rainfall significantly chills the upper parts of ash deposits, but compaction in simple cooling units ends before chilling by rainwater influences cooling of the interior of the sheet. Rainfall does, however, affect compaction at the boundaries of deposits in compound cooling units, because the influx of heat from the overlying unit is inadequate to overcome heat previously lost to vaporization of water. Three density profiles from the Matahina Ignimbrite, a compound cooling unit, are fairly well reproduced by the model despite complexities arising from numerous cooling breaks. Uncertainties in attempts to correlate in detail among the profiles may be the result of the non-uniform distribution of individual deposits. Regardless, it is inferred that model compaction is approximately valid. Thus the model should be of use in reconstructing the emplacement history of compound ash deposits, for inferring the depositional environments of ancient deposits and for assessing how long deposits of modern ash flows are capable of generating phreatic eruptions or secondary ash flows.