In order to explore formulation design theory and methods for high energy insensitive polymer bonded explosives(PBXs), the general mathematical model of multi-objective nonlinear optimization design for high energy insensitive PBX formulations was proposed, based on the investigation of structure-property relationship for PBXs. The empirical functions of sensitivities versus compositions of TATB/HMX-based PBX formulations were acquired from experimental data. And a specific mathematical model for HMX/TATB based PBXs was set up accordingly, using the cylinder specific kinetic energy function, impact sensitivity function and shock sensitivity function as multiple objective functions, with the energy level, sensitivity level and the content bounds as constraint conditions. Ten PBX compositions of 8 energy levels were designed and their energies as well as sensitivities were predicted according to the specific mathematical model. Four of the 10 compositions were selected to be tested. As a result, the error of the prediction values for energies and shock sensitivities according to the design model deviates within 5% and 6% respectively, while the prediction values of impact sensitivities are in the same level with experimental results.