Mercury's neutral sodium exosphere is simulated using a comprehensive 3D Monte Carlo model following sodium atoms ejected from Mercury's surface by thermal desorption, photon stimulated desorption, micro-meteoroid vaporization and solar wind sputtering. The evolution of the sodium surface density with respect to Mercury's rotation and its motion around the Sun is taken into account by considering enrichment processes due to surface trapping of neutrals and ions and depletion of the sodium available for ejection from the surfaces of grains. The change in the sodium exosphere is calculated during one Mercury year taking into account the variations in the solar radiation pressure, the photo-ionization frequency, the solar wind density, the photon and meteoroid flux intensities, and the surface temperature. Line-of-sight column densities at different phase angles, the supply rate of new sodium, average neutral and ion losses over a Mercury year, surface density distribution and the importance of the different processes of ejection are discussed in this paper. The sodium surface density distribution is found to become significantly nonuniform from day to night sides, from low to high latitudes and from morning to afternoon because of rapid depletion of sodium atoms in the surfaces of grains mainly driven by thermal depletion. The shape of the exosphere, as it would be seen from the Earth, changes drastically with respect to Mercury's heliocentric position. High latitude column density maxima are related to maxima in the sodium surface concentration at high latitudes in Mercury's surface and are not necessarily due to solar wind sputtering. The ratio between the sodium column density on the morning side of Mercury's exosphere and the sodium column density on the afternoon side is consistent with the conclusions of Sprague et al. (1997, Icarus 129, 506–527). The model, which has no fitting parameters, shows surprisingly good agreement with recent observations of Potter et al. (2002, Meteor. Planet. Sci. 8, 3357–3374) successfully explaining their velocity and column density profiles vs. heliocentric distance. Comparison with this data allows us to constrain the supply rate of new sodium atoms to the surface. We also discuss the possible origins of the strong high latitude emissions (Potter and Morgan, 1990, Science 248, 835–838; 1997a, Adv. Space Res. 19, 1571–1576; 1997b, Planet. Space Sci. 45, 95–100; Sprague et al., 1998, Icarus 135, 60–68) and the strong variations of the total content of the sodium exosphere on short (Potter et al., 1999, Planet. Space Sci. 47, 1441–1449) and long time scales (Sprague et al., 1997, Icarus 129, 506–527).