Objective In order to design a quick disassembling wirebound box to meet the requirements of compressive property and lowest overall cost. Methods According to the storage and transportation conditions, the box structure and member sizes were preliminarily designed. Objective function of box materials was built with the cleat thickness as a variable. And then a new objective function was built with the strength conditions of horizontal cleats and vertical cleats as constraint conditions. Finally, the variable of original objective function was solved. Results Through the Lagrange multiplier method, the thickness of horizontal cleats and vertical cleats must be greater than 35 mm and 20.4 mm, respectively. With the help of SolidWorks modeling and finite analysis, the stress, displacement, mass and volume of six kinds of solid wood boxes and plywood boxes with cleats thickness of single 36 mm, single 21 mm, and double 21 mm respectively were compared and the comprehensive situation of plywood box was found to be the optimal. So the plywood box with middle cleats of double 21 mm was selected. Compression test and stacking test verified the results of simulation test. Conclusion Mathematical optimization method and computer finite element method provided a good method and means for optimization of structural design of quick disassembling wirebound box. The research results also provided effective theoretical and practical basis for the development of wirebound box in the domestic market.