The structural framework of the Val d’Agri region results from the superposition of different deformation events over time. In this area, the largest European onshore oil field was discovered in the 1980s, and since then, much geologic and geophysical data have been collected. However, the structural complexity and the poor quality of subsurface data have prevented a full understanding of fault evolution and kinematics so far. In this study, scaled sandbox analogue models have been used to better understand the role of syn-rift inheritance in the present-day structural architecture and to test different possible mechanisms of interaction between inherited transpressional structures at depth and newly formed extensional fault systems at shallow levels during regional quaternary extensional tectonics. Analogue models included two consecutive sinistral transpressional phases deforming the basement and the overlying Apulian Platform carbonates, affected by preexisting northeast–southwest-oriented extensional fault zones. The third phase of the experiments consisted of extensional reactivation of the previously formed transpressional structures. Different kinematic solutions were used to investigate the causal relationships between deep and shallow deformation structures. The very good similarity between the experimental results and the natural prototype strongly supports the presence at depth of a main northeast–southwest-oriented syn-rift extensional fault zone, which was affected by positive inversion during the transpressional deformation of the Apulian Platform below the Val d’Agri area. Comparison of experimental results with fault patterns interpreted on available seismic lines indicates that, despite that no direct connection from deep to shallow faults has been recognized, some structural control of the fault pattern at depth on the evolution of the Val d’Agri quaternary extensional fault systems at shallow depth is possible. Extensional deformations at depth can be accommodated by newly formed faults or by the extensional reactivation of inherited high-angle transpressional fault zones.