We present an algorithm for computing all two disk-finger caging grasps along the boundary of a polygonal part with n edges. A grasp is said to cage a part when the fingers make it impossible for the part to move to a distant location-and, hence, escape the grasp-without penetrating a finger. Using the relation between immobilizing grasps (which prevent any motion of the part) and caging grasps we propose an algorithm with the desirable property that its running time depends on the actual size of the reported set of grasps (and less heavily on the complexity of the input, i.e., the description of part). In addition, the output set of all caging grasps along the boundary can be efficiently queried to check whether a given arbitrary two-finger grasp is caging.