The fixturing process for holding and locating workpieces on machine tools is essential in manufacturing systems. This process is one of the important factors affecting machining accuracy and has sofar been carried out manually by skilled workers. In order to realize fully automated manufacturing systems in the near future, particularly in small-batch machining and assembly, it is necessary to automate the fixturing process. One of the key factors in realizing an automatic fixturing process is to develop a fixturing support system. This system provides several important items of information for fixturing such as positions of fixtures and fixturing forces. In this study, a new fixturing support system is proposed. The elastic deformation of the workpiece caused by the fixturing force is analyzed by the finite element method, and the optimum fixturing position which gives the minimum form error of the surface to be machined is determined. The genetic algorithm is applied to the optimization process of the fixturing condition.