A device (10) for extracting biliary or urinary stones, calculi or the like (stones 104) from the biliary or urinary tract (100) of a patient including a catheter shaft (12), a first expandable apparatus for dilating the tract entrance or the sphincter thereat, and a second expandable apparatus for capturing the stone and/or urging it out of the tract. The first expandable apparatus may be an inflatable balloon (14) fixed on the catheter shaft (12), and the second expandable apparatus may be a second inflatable balloon (18) fixed on the catheter shaft or on a second tube telescopically associated with the catheter shaft, or may be a reversibly collapsible extraction basket (154) such as of nitinol wires, that is slidably receivable in and extendable from the catheter shaft (112). A device (210) for temporarily dilating a sphincter in a patient, such as the Sphincter of Oddi (102), includes an elongated catheter shaft (212) and an inflatable balloon (264) carried thereon and having a proximal portion (266), a distal portion (268) and an intermediate portion (270) therebetween. The intermediate balloon portion (270) has, upon inflation of the balloon (264), a diameter suited for temporary dilation of the Sphincter (102), while the proximal and distal balloon portions (266 and 268) have, upon inflation of the balloon (264), diameters greater than the inflated diameter of the intermediate balloon portion (270).