Methods for Monte Carlo simulation of planetary exospheres have evolved from early work on the lunar atmosphere, where the regolith surface provides a well defined exobase. A major limitation of the successor simulations of the exospheres of Earth and Venus is the use of an exobase surface as an artifice to separate the collisional processes of the thermosphere from a collisionless exosphere. In this paper a new generalized approach to exosphere simulation is described, wherein the exobase is replaced by a barometric depletion of the major constituents of the thermosphere. Exospheric atoms in the thermosphere-exosphere transition region, and in the outer exosphere as well, travel in ballistic trajectories that are interrupted by collisions with the background gas, and by charge exchange interactions with ionospheric particles. The modified simulator has been applied to the terrestrial hydrogen exosphere problem, using velocity dependent differential cross sections to provide statistically correct collisional scattering in H-O and H-H+ interactions. Global models are presented for both solstice and equinox over the effective solar cycle range of the F10.7 (80 to 230). Simulation results show significant differences with previous terrestrial exosphere models, as well as with the H distributions of the MSIS-86 thermosphere model. ¿ American Geophysical Union 1994