Container ports are critical components of global port and shipping supply chain (PSSC) systems. Their handling operation resiliencies can affect their performance, along with those of the overall port and shipping supply chain. According to the characteristics of the container handling operations, this study establishes a modeling paradigm for quantifying the resilience of handling chain system (HCS) in container ports. Considering the nonnegative arrive rate and the container handling completion rate, with the upper limit in real container port environments, nonlinear links have been added into the model of the HCS. The resilience of the HCS was analyzed according to the different pole distributions of unsatisfied freight requirement transfer function. Simulation results show that the upper limit of the container handling completion rate has a significant impact on the resilience of the HCS. The contributions herein demonstrate a starting point in the development of a quantitative resilience decision making framework and mitigating the negative impacts for port authorities and other players in the PSSC.