The invention relates to a snare device for catching an object, in particular for catching objects or foreign bodies in a human or animal body, comprising a hollow element, in particular a catheter, and a snare of a flexible elastic shape-memory material, wherein the snare can be moved relative to the hollow element and can be pulled into the hollow element and can be pushed out of the hollow element, and wherein the snare has a memorized original shape, to which the snare returns, when the snare is pushed out of the hollow element, by means of the material stresses caused when the snare is pulled in, and the hollow element has an outlet opening, which is arranged laterally on the hollow element and which is set back from the distal end of the hollow element and through which the snare can be pushed out of the hollow element and can be pulled into the hollow element.
