In this paper, the multi-agent containment problem is investigated. In particular, we focus our efforts on a continuation of our previous work on leader-follower networks, by imposing a hierarchical structure on the network topology. The main idea is to organize the team of autonomous, mobile agents in a multi-layered structure, which enables us to understand the tradeoffs between performance and complexity of the hierarchical topology, and we achieve this in the setting where we drive the collection of mobile agents to a target location while guaranteeing containment. In other words, the movement should be such that each layer stays within the convex hull of its parent layer while keeping its child layer inside its own convex hull. Such a criteria is to ensure that the movement of all the agents is constrained to a limited area while the group is moving. The application of this arises, for example, in surveillance, demining, and hazardous materials removing.