Very large magnitudes of explosive volcanic eruptions can produce giant ash clouds with diameters of hundreds to thousands of kilometers. These ash clouds are controlled by gravity and rotational forces, leading to a more radially constrained shape than clouds produced by smaller eruptions. Here we develop a dynamic model of the formation of large ash clouds that are produced by eruptions of constant intensity and finite duration, incorporating source latitude, eruption type, magnitude, and intensity. The cloud grows as a stratified intrusion in the stratosphere to an equilibrium shape that approximates an ellipsoid of revolution, rotating anticyclonically as a solid body, at sufficient large distances from the equator. More generally, the structure of the cloud is determined by the source latitude λs and the parameter Ys = ys(β/Nd0)1/2, wherein ys is the distance of the source from the equator, β is the north-south gradient of the Coriolis frequency, N is the buoyancy frequency of the stratosphere, and d0 is the maximum cloud thickness. A steady solution for an equilibrium cloud exists if Ys lies above a boundary that ranges from π/2 at the equator to 0 at the pole. These clouds move westward at an increasing rate with decreasing latitude. Below this boundary steady solutions appear not to exist and the nature of the breakdown of the solution at the boundary suggests that the cloud, or part of it, moves toward and across the equator. The above parameters may be expressed in terms of latitude and cloud volume, which enables the model to be applied to the ash clouds of past large-magnitude eruptions. The results suggest that the behavior of clouds formed from plinian phases with eruption magnitudes M < 6.5 (M = log10m − 7, wherein m is the erupted mass in kilograms) depends on source latitude and eruption intensity, whereas for M > 6.5 they could achieve interhemispheric transport from most latitudes. For clouds from co-ignimbrite sources, for M < 7.5, cross-equatorial transport is only possible for sources in the tropics, but for M > 8, it is possible from most latitudes.