Negotiation is an essential process in material procurement to achieve a final agreement between contractor and supplier. Several researches attempt to improve the negotiation process of construction material procurement. For example, the use of genetic algorithm to identifying the joint pay-off that both parties agree. However, this method still has limitations due to the complexity of calculation and the difficulty of understanding. Meanwhile, the mathematical function is easy to understand and can be used as an alternative method to identify the optimum joint pay-off point. In addition, negotiation by each party may have a different target or weight on each issue. Thus, the issues for negotiation and weight of each issue should be studied and define as a guideline. This research aims to apply the mathematical functions for calculating the optimum joint pay-off that is agreed by both parties. Research started with questionnaire design and interview on the topics related to material procurement process, material buy from contractor and issues that are used for negotiating construction material. The result of interview with 35 experts on material procurement found that six important issues for material negotiation are price, advance payment, credit term, payment period, delivery mode and freight. Then, researcher selected the three materials for conducting case study. There are aggregate stone, cement and ready-mixed concrete. Next, the data is collected from in-depth interview with contractors and suppliers for identifying weight and developing the function between the percent pay-off and options in each issue. These functions were the foundation of identifying joint pay-off for negotiating material. The resulf from analytical hierarchical process (AHP) found that price is perceived as the most important issue whereas other issues are perceived the different weight due to the material type and the ability of contractor. In addition, the result found that the mathematical functions can be used to calculate the optimum joint pay-off for negotiating construction materials