This study focuses on the Alpine fold and thrust belt in the Ionian basin of Albania, where there are giant onshore oil fields. The evaporites have acted as a detachment layer but also have been cut by thrusts that carry evaporites to the surface in their hanging walls. Where the detachment is located at the top of the evaporites, they are dragged up in the footwall along thrusts, and faults develop at the base and the top of the evaporite. Simple shear deformation along the thrusts causes greater than 80% thinning of the evaporite, so that sheets of only 40-200 m thickness are preserved, whereas the original evaporite thickness probably was well in excess of 2000 m. Where ramps cut through the evaporite and cause repetition of the complete evaporite layer, the salt is remobilized into salt-filled compressional anticlines or escapes at the surface to produce smeared-out surface extrusions. The most spectacular example of this is the Dumrea structure, where the evaporites have developed into a complex shape from an overthrusted allochthonous sheet that has been extruded at the surface. The Dumrea structure is up to 5.6 km thick proved by drilling and has been displaced laterally by up to 25 km, and it has the effective geometry of a giant sheath fold.