Based on the mathematical modeling method, the reasonable transportation and packing of a typical special-shaped folding carton, triangular octagonal special-shaped folding carton was studied. Firstly, according to the modeling auxiliary dimensions of the carton, the mathematical model on its volume, surface area, related parameters of the contents and transportation space was deduced. Then, software programming was performed based on the derived mathematical models. After inputting the basic parameters of carton and transport packaging from the program interface, the optimal relevant parameter values of carton, contents and transport packaging could be generated as output. Using the optimal parameter values, physical proofing can be quickly performed in making cartons and transport packaging.