We present a geomechanical analysis of the Ordovician reservoir from the Tinzaouatine field situated in the prolific Illizi Basin, eastern Algeria. The sandstone reservoir has a hydrostatic pore pressure gradient (9.95 MPa/km). We analyzed a cumulative of 300 m of acoustic image log data and identified the coexistence of B-quality extensive drilling-induced tensile failures (DITFs) and compressive failures, i.e., breakouts (BOs), indicating a mean maximum horizontal stress ([Formula: see text]) orientation of N140°E. We used a combined BO and DITF-based solution to estimate horizontal stress magnitudes when the two failure types coexist. Based on the C-quality minifrac measurements, we interpreted the minimum horizontal stress ([Formula: see text]) gradient as 17.4–17.47 MPa/km, whereas the new approach indicates an [Formula: see text] range of 17.31–18.67 MPa/km. Using the BO width and DITF-based approaches, we inferred an [Formula: see text] gradient range of 28.37–38.59 MPa/km within the studied reservoir. Based on the relative stress magnitudes, we infer a strike-slip tectonic stress regime in the studied field.