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This paper is concerned with a caging problem: we wish to surround an object B by a multifingered hand such that B has some freedom to move, but still cannot escape the “cage ” formed by the fingers. We introduce a new notion of the caging set, which is based on the configuration-space representation of the free motions of the hand system with respect to the object. Using stratified Morse theory, we show that the hand’s configuration at which the cage is broken corresponds to a frictionless equilibrium grasp. This allows us to formulate a technique for computing the caging set of a two-fingered hand whose opening is controlled by a single parameter. The technique generalizes to one-parameter gripping systems having a higher number of fingers. 1