Strata adjacent to exposed diapirs in La Popa basin, northeastern Mexico, comprise stacked halokinetic sequences consisting of unconformity-bounded packages of thinned and rotated strata cut by radial faults. Deformation results from shallow drape folding over the flanks of the rising diapirs and not from deep drag folding in diapir-peripheral shear zones. Subsurface analogs from the Gulf of Mexico have diapir-flanking geometries ranging from similar, wide zones of upturned and thinned strata to undeformed, constant-thickness strata. Subhorizontal salt tongues display little subsalt deformation and thinning. We propose a general model for passive diapirism and flank deformation that includes (1) gradually varying salt-flow rates, (2) superposed episodic sedimentation that results in changing bathymetric relief, (3) rotation of near-surface strata as salt inflates relative to the adjacent basin, (4) failure and erosion of strata in the steepening bathymetric halo, and (5) bedding-parallel slip surfaces that converge on unconformities and onlap surfaces. A primary factor, influencing flank geometries is the width of the bathymetric high extending beyond the diapir edge. This is largely dependent on the thickness of the halokinetic sequence onlapping the diapir, which in turn is controlled mostly by the interplay between salt inflation/deflation rates and sedimentation rates. Other factors include the amount of concurrent shortening, which produces a wider but less intense zone of deformation, and the position on the scarp of salt breakout and extrusion. Our model is important for exploration and production in diapir-flank and subsalt settings because of its implications for trap size and geometry, reservoir distribution, trap compartmentalization and pressure seals, and hydrocarbon charge. It can help in explaining complex and enigmatic well data and in better assessing risk in areas of poor seismic imaging.