The term hyper-redundant refers to redundant manipulators with a very large or infinite number of degrees of freedom. These manipulators are analogous in morphology to snakes, elephant trunks, and tentacles. While a variety of obstacle avoidance algorithms for nonredundant and mildly redundant manipulators exist, little analysis has been performed for hyper-redundant robots. This paper presents a strictly geometric algorithm for hyper-redundant manipulator obstacle avoidance which relies on the use of “tunnels” in the obstacle-filled workspace. Methods of differential geometry are used to formulate equations which guarantee that sections of the manipulator are confined to the tunnels, and therefore avoid obstacles. A general formulation is presented with an example to illustrate this approach.