ICESat elevation profiles of tabular iceberg margins and the Ronne Ice Shelf edge reveal shapes indicative of two types of bending forces. Icebergs and shelf fronts in sea-ice-covered areas have broad (~1000 m wide), rounded, ~0.6 m high 'berms' and outer edges that slope down several meters toward the water. Bergs in warmer water have 2 to 5m 'ramparts' with ~1500 m wide edge-parallel 'moats' inboard of the edge. This latter pattern was first revealed in images from International Space Station (ISS) showing edge-parallel melt ponds on one iceberg just prior to its disintegration. Model results indicate the patterns are caused by hydrostatic and lithostatic forces acting on the ice face. 'Berm' profiles arise from differences between ice and water pressure along the face. 'Rampart-moat' profiles result from waterline erosion, creating a submerged bench of ice that lifts the ice edge. We use the results to discuss iceberg breakup at low latitudes.