Three-dimensional (3-D) seismic imaging techniques are used to identify a series of 21 deformed fluid escape pipes that transected a 1500-m-thick salt sheet at regular intervals over the past 1.7 m.y. By reconstructing these pipes to their original vertical cylindrical geometry, we show that the salt sheet deformed by Couette flow over this period. The average flow velocity of the top boundary of 2 (±0.3) mm/yr, equates to a bulk viscosity for the sheet of 2.3 × 1018 Pa·s, within the range obtained from field and laboratory measurements. Similar fluid escape structures are expected to occur widely in salt basins due to the extreme fluid overpressure developed beneath the almost-impermeable salt. These structures offer a new approach for constraining basin-scale models of the kinematics of salt flow by the in situ measurement of flow geometry, with the potential to provide calibrations for experimentally derived flow laws for evaporite systems.