In this article, distributed finite-time tracking control for nonlinear multi-agent systems subject to external disturbances is investigated. With the aid of sliding-mode control technique, both the finite-time consensus tracking in the presence of a single leader and the finite-time containment control with multiple leaders are in detail analysed. A distinctive feature of this work is that the communication topology among the followers can be directed. It is shown that the states of the followers can track that of the leader when there exists a single leader, and converge to a convex hull spanned by those of the leaders when there exist multiple leaders, both in finite time. Moreover, the finite convergence time is explicitly presented. Numerical examples are finally given to illustrate the theoretical results.