The circumplanetary flow of Io's SO2 atmosphere is modeled using the direct simulation Monte Carlo (DSMC) method. This how develops as gas sublimates from SO2 frost in the warm subsolar region and flows toward the colder night-side, where it condenses. The axisymmetric model presented extends from the subsolar point past the terminator into the night-side. The remaining portion of the night-side atmosphere is assumed to be static. The DSMC method solves the fully viscous and compressible, non-local thermal equilibrium (non-LTE), rarefied flow problem by statistically extrapolating from the motions and collisions of representative molecules. Heating due to neutral plasma bombardment and cooling by non-LTE radiation are modeled. Quantities of a second, non-condensible gas are also added to simulate the possible effects of H2S or O-2 in the atmosphere. It is found that, except in the subsolar region, the flows are predominately rarefied. For high subsolar temperatures, the atmospheric how may become supersonic and then decelerate through a diffuse, oblique shock upstream of the terminator. Appreciable local condensation occurs below the shock while the atmosphere above the shock is significantly inflated. These hydrodynamic features, among others, have implications for the observations of frost cover, atmospheric how, and the ionosphere. (C) 2000 Academic Press.