Drag folds bordering salt diapirs are commonly attributed to shear from rising salt. Finite-element models demonstrate that shear deformation is only significant for extremely weak overburdens, such as those having high overpressure and ductile interlayers. Protrusions of overburden into and onto the diapir are most susceptible to folding. So-called drag folds are much more likely to initiate as drape folds of strata onlapping a downbuilding diapir, here termed flap folds for clarity. Potential for flap folding is greatest where the salt/overburden contact dips moderately and for episodic or variable timing and thickness of deposition. Moderate dip allows strata to onlap far across the diapir crest and be carried upward into a high-amplitude fold with the rising salt. Depositional hiatuses allow time for such rise without additional layers that would strengthen the onlapping wedge. Previously folded strata may block onlap of later layers. Stretching and rotation of the layers adjacent to steep parts of the diapir may cause disaggregation, slumping, and debris deposits that can be overridden as the diapir crest spreads laterally onto the overburden surface. Large changes in the relative rates of salt rise and sediment deposition can create cycles of onlap, flap folding, and spreading.