The authors report 5 cases (3 women and 2 men) of extrinsic stenosis of the coeliac axis by the arcuate ligament of the diaphragm. In one of the latter, the stenosis of the coeliac axis was associated with chronic calcific pancreatitis. These 5 patients were operated on. Division of the arcuate ligament gave on the whole very favourable results. (3 excellent results, one good and one average result). The authors then recall the clinical, angiographic and pathogenic data in this disease which remains exceptional. The diagnosis should be made and operation decided only after a fairly long period of observation during which one has elimiatned the diagnoses of gastro-intestinal, gall bladder, pancreatic and above all psychiatric disease by endoscopy, radiography and symptomatic medical treatment.