We examine three-dimensional seismic data from the Santos Basin, offshore Brazil, to determine how, where, and when radial faults grow near a salt diapir. We show roof stretching alone cannot account for the large heights and lengths of the kilometer-scale radial faults, suggesting stock widening (‘stem push’), a mechanism implied in numerical models but not yet recognized in natural examples, played a pivotal role in fault formation. We suggest that, when a diapir is covered by a roof, radial faults form due to roof stretching, extending no further than the limit of the drape folding. The roof may then be shouldered aside and the faults buried along the stock flanks, exposing these strata to stem push–related stresses that may then re-activate preexisting, or form new, radial faults. We suggest the causal mechanism for radial fault formation will likely change as roof thickness varies during diapirism, with this reflecting the ratio between sedimentation rate and salt volumetric flux.