Environmental consciousness has become critical in the design and operation of globally integrated supply chain networks. This research examines the carbon footprint across supply chains and thus contributes to the knowledge and practice of green supply chain management. The analytical model uses the long-range Lagrangian and the Eulerian transport methods. Analytical and finite difference methods are used to approximate the three-dimensional infinite footprint model. A simplified numerical example validates and illustrates the proposed approach. The results show that carbon emissions across stages in a supply chain can constitute a significant threat that warrants careful attention in the design phase of supply chains.