We propose a solution to the problem of herding by caging: given a set of mobile robots (called herders) and a group of moving agents (called sheep), we guide the sheep to a target location without letting them escape from the herders along the way. We model the interaction between the herders and the sheep by defining virtual “repulsive forces” pushing the sheep away from the herders. This enables the herders to partially control the motion of the sheep. We formalize this behavior topologically by applying the notion of caging, a concept used in robotic manipulation. We demonstrate that our approach is provably correct in the sense that the sheep cannot escape from the robots under our assumed motion model. We propose an RRT-based path planning algorithm for herding by caging, demonstrate its probabilistic completeness, and evaluate it in simulations as well as on a group of real mobile robots.