Cascade failure is a common phenomenon in supply chain networks, where the environmental uncertainty injects a layer of significant complexity into the dynamics of the failures. This paper addresses this challenge by proposing a novel cascading failure model that incorporates noise interference. The model, grounded in complex network theory, aims to analyze the impact of environmental uncertainty on the propagation of cascading failures within supply chain networks. Simulation results demonstrate that noise disturbances exacerbate the cascading failure process by increasing the critical threshold and accelerating the decomposition of the network structures. Interestingly, the influence of noise diminishes as the heterogeneity of load redistribution increases. Additionally, the study delves into the impact of both initial load parameters and load redistribution parameters on the critical threshold. Our findings reveal that by strategically adjusting these two parameters, a minimum critical threshold can be achieved, potentially enhancing network resilience.