Flexure hinges are widely used as joint linkages for precision stages applied to lithography processes. Among them, precision stages with 3 DOF (Degrees of Freedom) of x, y and θ_z prevail in semiconductor manufacturing and they have been adopting single directional flexure hinges as mechanical linkages without backlash and debris. However, new technologies including nano-imprinting, which replaces lithography, needs more than 3 DOF precision positioning stages that adopt cylindrical flexure hinges. In this study, the cylindrical flexure hinges with circular notches were analyzed using the Timoshenko beam theory and FEM (Finite Element Method), with focused on their directional stiffness. Based on the analysis and result comparison between theoretical equations and FEM, several practical suggestions for determining important design variables are provided in the conclusion of this study.