To analyze the robustness of complex interdependent supply chain networks suffering disruption events, the cascading failure mechanism of both intra-network and inter-network is studied. Without loss of generality, the undirected information layer network and directed physical layer network comprising the interdependent supply chain network are generated via the stochastic rule. Then, the network characteristics, i.e., node load and node capacity, are expressed by parameters α, β, σ, etc. The redistribution strategies of failure loads corresponding to the condition of existing edge flow constraints are presented. Through giant component functions, the valid nodes still with function could be judged when the redistribution is finished. Furthermore, the time-varied state equations are constructed based on one to one interdependent relationship between the cyber-layer network and physical-layer network, which can depict the dynamic propagation throughout the interdependent supply chain network. Finally, numerical simulations including two cases: single node removal and multi-node removal, are given and the robustness of interdependent supply chain networks with different parameters is compared. In particular, multi-node removals are classified in three ways, i.e., degree ascending, degree descending, and random degree. The simulation results show that the multi-node removal in the ascending degree way leads to the worst robustness performance among the three removal ways, if β = 0. 5, 1, 1. 5, 2. Meanwhile, the first phase transition of the cascading failure for interdependent supply chain networks, after multi-node removal, is more obvious than for isolate layer networks, i.e., a small fraction of nodes removal will result in the crash of the whole interdependent supply chain network.