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Under the fixed directed topology, this paper studies the finite-time containment control problems of multi-agent systems with multiple static or dynamic leaders. Assuming that there is no information interaction between leaders, a control algorithm based on fast terminal sliding mode is proposed, which drives the followers" motion trajectories to converge to the convex hull composed of leaders in a finite time. Moreover, considering the fact that leader’s velocity can not obtained online in practiced applications, observer based finite-time containment algoriths are given. By using graph theory and Lyapunov stability theory, sufficient conditions of finite-time containment control are derived. Finally, simulation examples are given to illustrate effectiveness of the proposed algorithms.