In the wind tunnels, the balance measurement instrument is used to measure six components of force and moment on an airplane model. The balance of measurement consists of two parts of the balance structure and electronic equipment. In this research, a mechanism with flexible hinges is designed to achieve the desired configuration of the balance structure. In the process of designing the geometric structure of this mechanism, an effective arrangement has been implemented for the six load cell - flexure columns. The advantages of flexible hinges in comparison to conventional hinges are the absence of friction, compactness and its linear behavior. The reaction effects of the components of force and moment on each six load cell - flexure columns created the coupling errors. One of the main sources of this kind of error is related to the structure of the balance mechanism. The reason for this type of error is the inadequacy of the axial flexibility to the lateral flexibility of the columns. The aim of this research is to optimize the design of the flexible mechanism in order to achieve the minimum coupling error of the structure. For this purpose, hinge design considerations and analytical equations of the flexible mechanism have been extracted. The design of the balance mechanism is optimized by creating a structure coupling error matrix. To validate the analytic equations and results, the problem is compared with the finite element analysis. The results indicated that the measurement errors decrease in the measurement of six components of force and moment of balance.