Models are presented for the physical processes that occur in the formation of pyroclastic flow generated by the gravitational collapse of a vertical eruption column. The main controlling parameters are considered to be the vent radius (R), gas content (N), and initial velocity (W) of the gas. For the ranges R=50 to 600 m, N=0.5 to 5% gas, and W=200 to 600 m/s, column collapse is modeled as an inverted turbulent jet, modified by including expressions for the efficiency of heat transfer between air and small pyroclasts. Entrainment of air during the collapse can result in initial cooling of the flow by up to 350¿C. The variation in the amount of cooling is considered to account for the considerable ranges of emplacement temperatures and the widely differing degrees of welding observed in different ignimbrites. High emplacement temperatures are favored by eruption columns with low gas contents and low gas velocities, whereas low emplacement temperatures are favored by eruption columns with high gas velocities and high gas contents. The initial stages of flow are modeled as a highly turbulent, low-particle-concentration density current. Numerical solutions of the turbulent stages of flow are presented assuming uniform radial spreading from a central source (the vent). Flows from large eruptions may still have velocities of up to 100 m/s at distances of tens of kilometers from the source. The methods have also been applied to uphill flow and demonstrate that flows produced at high volume rates of eruption can surmount topographic barriers of several hundred meters at distances of several tens of kilometers from the vent and explain the spectacular mobility of some large pyroclastic flows. Turbulent suspension in a gas flow with a low concentration of particles is not a viable mechanism of particle transport, as many of the clasts (about 1 mm) found in the depositis have terminal velocities well above the shearing stress velocities of even a rapidy moving gas flow (v*=1 to 12 m/s). The flows are deduced to segregate into a high-concentration basal zone within a a few kilometers of the vent, as larger clasts settle to the base of the flows. Fines are thought to be generated by crushing within the high-concentration basal zone and are fluidized by exsolving gases to produce a pyroclastic flow with high concentrations of fluidized particles. The upper dilute part of the flow and the fine ash elutriated by fluidization contribute to the formation of widely dispersed ash fall deposits which are as voluminous as the associated ignimbrite. The flows are capable of transporting clasts of several centimeters or tens of centimeters to tens of kilometers distance. The motion of the dense lower part (the pyroclastic flow) disassociates itself from the upper turbulent cloud of fine ash and gas, which eventually mixes with the atmosphere sufficiently to form a convective plume.