We study the robust containment control problem for second-order multi-agent systems with unknown time delays, considering both the agent's communication delay and inter-agent delay, simultaneously, We derive the maximum delay range for undirected topology and directed topology respectively, such that multi-agent systems can maintain the robust containment. Via the convex analysis and nonlinear programming, the analytic maximum delay range to maintain containment under undirected graphs is derived. For the directed graph, the genetic algorithm is proposed to solve the non-smooth optimizing problem and the numerical values of maximum delay range are obtained. Meanwhile, the results can be reduced to find the maximum delay range of leader-following control. Finally, the effectiveness of the proposed algorithm are verified via the simulations.