Gravity and high-resolution aeromagnetic maps reveal the three dimensional geometry and subsurface structure and lithology of the basement beneath the Tucson Basin, Arizona. Limited drill hole and seismic data indicate that the maximum depth to the basement is approximately 6000 meters and that the sedimentary sequences in the upper 3000 m of the basin were deposited during the most recent extensional episode that commenced about 13 Ma. The negative density contrast between these Neogene and Quaternary sedimentary sequences and the adjacent country rock produces an isostatic residual gravity low, whose steep gradients clearly define the lateral extent of this part of the basin. The aeromagnetic maps show large positive anomalies associated with deeply buried Jurassic(?) plutons, Cretaceous and Tertiary volcanic rocks at and below the surface of the basin, and buried and exposed dikes. The magnetic anomalies therefore give us insight into the older and deeper structures of the basin. Simultaneous 2.5-dimensional modeling of both gravity and magnetic anomalies constrains the thickness of the basin and the dips of the buried faults that bound the basin. The resulting volume estimates for the young part of the basin combined with knowledge of the fault dips help constrain the amount of extension the basin has accommodated in the last 13 Ma.