The geometries and kinematic evolution of 3-D inversion thrust structures have been modeled using 3-D sandbox analogs of hanging-wall deformation above footwall blocks with both concave-up and convex-up listric geometries. Extension over 3-D concave-up listric detachments produced characteristic rollover anticlines and crestal-collapse graben systems that parallel the along-strike, sinusoidal or cuspate plan geometries of the detachment breakaways. Three-dimensional inversion by horizontal contraction produced asymmetric, thrust-fault-bounded, hanging-wall inversion anticlines with curved axial traces that also follow the plan-view shape of the extensional breakaways. The main detachments were reactivated during the inversion, and new, steep thrust segments propagated upward from the detachment breakaways. Shallow to moderately dipping hanging-wall back thrusts also propagated outward from the crestal-collapse graben systems. The periclinal inversion anticlines exhibited two plunge culminations above the most concave sections of the main detachment surface. Extension above a 3-D convex-up, listric detachment surface produced a hanging-wall syncline together with a narrow, complex crestal-collapse graben system. In plan view, the axes of the hanging-wall syncline and the crestal-collapse graben formed parallel to the sinusoidal detachment breakaway. Inversion of this system produced a broad, thrust-fault-bounded anticline that shows along-strike plunge culminations. The main detachment surface was reactivated, and a moderately dipping thrust propagated upward through the syninversion strata. Segmented, hanging-wall back thrusts formed subparallel to the main detachment breakaway. Vertical and horizontal sections through the completed models were used to construct 3-D synoptic models for these inversion systems. The results of the analog experiments compare well with published examples of 3-D inversion structures from petroleum basins in the North Sea, Indonesia, and Argentina.