Resilience, the ability to withstand disruptions and recover quickly, must be considered during system design because any disruption of the system may cause considerable loss, including economic and societal. This work develops analytic maximum flow-based resilience models for series and parallel systems using Zobel's resilience measure. The two analytic models can be used to evaluate quantitatively and compare the resilience of the systems with the corresponding performance structures. For systems with identical components, the resilience of the parallel system increases with increasing number of components, while the resilience remains constant in the series system. A Monte Carlo-based simulation method is also provided to verify the correctness of our analytic resilience models and to analyze the resilience of networked systems based on that of components. A road network example is used to illustrate the analysis process, and the resilience comparison among networks with different topologies but the same components indicates that a system with redundant performance is usually more resilient than one without redundant performance. However, not all redundant capacities of components can improve the system resilience, the effectiveness of the capacity redundancy depends on where the redundant capacity is located.