Understanding the contemporary stress field and its variations is important in hydrocarbon production. These fluctuations are significant for borehole stability and trajectory, hydraulic stimulation, fault reactivation, and optimal well completion. In this study, we provide the first geomechanical model to determine the orientation and magnitude of the present-day stress of the Hassi Terfa field using geophysical logs to understand the origin of the spatial variation of the stress state. The breakouts from acoustic image logs provide an average maximum horizontal stress (SHmax) orientation of N115°, consistent with the Africa–Eurasia plate motion, which imposes the largest first-order stress source. However, our analysis demonstrates local stress perturbations near faults. This may mean that the stress field in the Hassi Terfa is superimposed by a third-order source of stress (<100 km). Our model demonstrates variations in stress magnitude with depth interpreted to be lithology-dependent, which act as a natural barrier against fracture propagation. We propose a new approach to quantify these perturbations via the stress regime index R′, using the magnitude of the principal stress components. The results demonstrate different layer-to-layer faulting regimes. These perturbations will limit the vertical propagation of hydraulic fracturing to the overlying formation, which enables it to access a larger reservoir volume and improve production. In general, a strike–slip regime with a slight normal slip component is interpreted for the study area. We develop the first-ever quantitative stress map using the relative principal stress magnitude parameter (Aϕ) to present the lateral variation of the stress regime throughout the Saharan platform. Results demonstrate a consistent strike–slip to normal/strike–slip regime with a uniform SHmax orientation. This map will help operators achieve optimal well direction and optimize hydraulic stimulation. Our results have considerable implications for hydrocarbon production in the central and southeastern Saharan platform.