The Termit basin is a Mesozoic-Cenozoic rift basin developed along the Central African Shear zone, it is formed under the tectonic setting of the opening of the Atlantic Ocean during the Early Cretaceous. The Termit basin underwent three stages of tectonic evolution--"rift-depression-rift" and two phases of rifting that formed two different fault strikes from Cretaceous to Paleogene. Based on the geological setting of the Termit basin, the mechanics of the basin is investigated through the analysis of the stress field using linear elastic theory with two dimensional finite element modeling, through the analysis of the stress field. The modeling results suggest that a series of NW-SE faults were developed at the west part of the Termit basin under the effect of the Early Cretaceous NE-SW regional stress field. The direction of the regional stress changed to nearly W-E in Paleogene. A series of N-S faults were formed at the SE part of basin where there were no pre-existent faults. The change in fault strike from near N-S trending to NW-SE trending in the place that had pre-existent faults was caused by the local stresses of the Early Cretaceous faults.