Finite time estimation and robust containment control are studied for second order directed networks considering nonlinear disturbance and unmeasurable velocities of followers. A novel distributed architecture is proposed including estimation layer, control layer and followers layer. The power estimator and sliding mode estimator are designed to achieve the accurate estimations of network errors in finite time based on finite time stability theory and equivalent output injection thought. Then nonsmooth control protocol is developed by applying homogeneity theory and sliding mode method, so as to make followers converge and remain in the dynamic convex hull formed by the leaders in finite time and suppress disturbance effectively. Simulation results verify the correctness of the theoretical analysis.