The solution of the governing transport equations for transient volatile behavior in a cooling pyroclastic deposit reveals dominant mechanisms that control cooling and degassing. the numerical model and algorithm presented here are time accurate and suitable for operation on a personal computer. This model takes into account the combined effects of cooling and low volatile outfluxing on the pressure, temperature, and volatile mass content in a deposit. Sample deposit simulations compare favorably with observations made by Kozu (1934) and Kienle and Swanson (1980). Other exemplary calculations of 20- and 40-m thick pyroclastic deposits indicate that the time required for total volatile outflux (approximately 21 and 83 days, respectively) is small compared with that required for the cooling effects of the upper and lower margins to come in contact (in excess of 70 and 265 days, respectively). The thermal behavior of the modeled deposits appears to be dominated by diffusive heat transfer, while the pressure field and volatile content within each sheet are dominated by hydrodynamic effects. ¿ American Geophysical Union 1990