Understanding the 3D geometry and evolution of extension-related folds is important because they may document the geometry and evolution of the associated faults, influence sediment routing and accommodation development, and may represent targets for hydrocarbon exploration or CO2 storage. Previous work on extension-related folds has largely been restricted to a 2D plane of observation; in this study we use 3D seismic reflection data from the Gulf of Suez, Egypt to determine the 3D geometry and evolution of fault-parallel folds during dip linkage of a vertically segmented extensional fault array that is locally decoupled across a salt-bearing interval. The 3D geometry of individual faults in the array and adjacent hanging-wall folds varies along strike; rollover structures occur above listric faults, whereas fault-bend folds occur above faults that have a ramp–flat–ramp geometry. Quantitative analysis of fault–fold attributes (e.g. fold amplitude) and the growth history of the fault array indicate that fault shape is controlled by the style of dip linkage, which in turn is controlled by the lateral separation of sub- and supra-salt segments prior to linkage. Small lateral separation yields a relatively subtle change in the overall convexity of the listric fault, whereas larger lateral separation results in a ramp–flat–ramp fault geometry, with the layer-parallel detachment lying within the salt. This study provides a link between fault spacing, style of dip linkage, final fault shape and, ultimately, the style of hanging-wall folding in mechanically layered stratigraphy. Our study indicates that 3D seismic reflection data have the ability to provide us with new 3D insights into the variability of, and controls on, the geometry and evolution of fault-related folds.