A mathematical model of the pressure gradient of supercritical CO2 in a vertical tobacco bed was developed in this study. In particular, the compaction of the tobacco as a function of temperature and CO2 flow is included in the model. Downflow of CO2 (low condition is described. At velocities in excess of 0.6 cm/sec at 7$0^{circ}C$, there is a large increase in pressure gradient for beds deeper than about 0.5 m. The proposed model offers a better understanding of operating the process using supercritical CO2.