Mathematic model of special-shaped folding carton was established, which described the relationship among body boards. The relevant 3D coordinates were established and homogeneous coordinates were applied to express the position of points. The relationship between the folding carton′s shaped angle and the body boards′ folding angle after forming was deduced by multiplying the coordinates of points and transition matrix. This mathematic model can be a foundation to calculate the carton's volume, capacity, relative cushion structure design, and interrelated software development.