In this paper, a leader based containment control strategy for multiple unicycle agents is introduced. Similar results for the single integrator case examined in  are derived based on the theory of Partial Difference Equations on graphs established in . The leaders converge to a desired formation based on a control law that is independent of the followers' states. Once the leaders have reached the desired formation, the followers converge to the convex hull of the leaders final positions. When the desired leader formation is infeasible, then (as was shown in ) the leaders converge to a configuration where they share the same velocities and orientations. We show in this paper that in such a situation, the followers converge to the same velocities and orientations as the leaders, with the same control law that was used for the followers in the initial containment control problem. The theoretical results are verified through computer simulations.