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, said snare device comprising a hollow element, in particular a catheter, and a snare made of a flexible elastic shape-memory material, wherein the snare is movable relative to the hollow element and can be pulled into the hollow element and pushed out of it, and wherein the snare has an impressed original shape to which said snare return, when pushed out from the hollow element, as a result of the material stresses caused when it was pulled in, wherein the original shape of the snare has a twisted area, as a result of which a first loop and a second loop are formed, wherein the first loop is arranged substantially parallel to the longitudinal axis of the hollow element, and the second loop is at an angle with respect to the longitudinal axis of the hollow element, and which is characterized in that the snare thus deformed is introduced into the hollow element and is arranged inside the hollow element, in that the second loop is pivoted relative to the first loop and through the first loop, such that the second loop, on emerging from the hollow element, pivots back through the first loop as a result of the load being removed from the shape-memory material, thereby allowing the object to be enclosed.