A surgical snare device for engaging an object in a body passage and that employs multiple loops for snaring the object. The loops, which can be made from a single elongated line or separate lines, are positioned at locations that substantially span across the diameter of the body passage. A tubular membrane cap is included which is made from a liner coupled with structural elements made of expandable wire for support. The membrane cap is selectively deployed from a sheath and radially expandable to envelop the captured object so that withdrawing the object is more secure and any sharp edges on the object do not damage walls of the body passage. The loops and membrane cap can be made from a metal, a metal alloy, or polymer. Perforations can be formed in the liner to allow fluid to pass through the membrane cap.
