When complex and thin-walled workpieces produced for the aircraft industry are machined, they are supported by fixtures to prevent them from easily deforming or vibrating. To support the workpieces effectively, the stiffness of the fixture should be sufficiently high. However, the criteria required for the fixture dynamics to support a workpiece without deformation and vibration during machining have not been thoroughly investigated. To minimize trial and error, the design parameters required for the fixture should be determined theoretically. Accordingly, this study proposes a method for theoretically determining the design parameters of a fixturing system. The effect of the substructure thickness on the dynamics of the entire structure was evaluated quantitatively using a theoretical model, and the validity of the model was verified experimentally. The stiffness of the entire fixturing system was estimated using the receptance coupling method. In addition, the relationship between the thickness of the substructure and stiffness of the entire structure was evaluated.