Abstract Three-dimensional seismic data from the Levant Basin, eastern Mediterranean, was used to quantify longitudinal strains in thick, multilayered Messinian evaporites at an early stage of salt tectonics. Gravity-spreading is driven by basin subsidence and tilting of the Levant margin and by progradation of the Nile Cone. Similar styles of shortening in two separate 3D survey areas comprise detachment folds, thrust-ramp folds and conjugate arrays of strike-slip faults. These Pleistocene structures can be explained with a single deformation phase with a tectonic transport direction of NE to ENE, obliquely opposed to the extension updip, which began in the Late Pliocene. Four major detachments within the Messinian are probably halite-rich intervals in the multilayer. Shortening of competent interlayers varies from 1–2% near the base to c. 7% near the top of the Messinian, with a sharp reduction in shortening at the top Messinian and roof to 1–2%. This shortening profile is attributed to asymmetric Poiseuille flow, indicating that salt is flowing downdip faster than the overburden is translating. Physical modelling supports the inferred flow profile, showing that each mobile layer flows faster than adjoining competent layers and that strains in evaporites can be far greater than in the overburden. This is the first published use of seismic data to demonstrate the flow regime within salt on a regional scale.