A device for cryoablating exposed tissue having a contoured contact surface includes a tube-shaped shaft and a flexible, thermally conductive enclosure that is attached to the distal end of the tube-shaped shaft. The enclosure is formed with a wall having an outer surface for contacting the target tissue and an inner surface which establishes and surrounds a cryochamber. A shapeable element is attached to the distal end of the shaft and extends into the cryochamber. The element can be permanently deformed into a pre-selected shape to cause a portion of the enclosure wall to conform to the contour of the target tissue. A high-pressure tube in the shaft passes a refrigerant through the shaft for expansion into the cryochamber. This expansion cools the wall of the enclosure, which in turn, extracts heat from the target tissue resulting in the cryoablation of the target tissue.