Abstract: Flexible hinges are widely used as one of the essential components to micro-motion robotics. Its rigidity directly has an influence on the positioning and operation precision of micro-motion robotics' ending pose. However, due to the diversities and complexities of practical demands, its geometrical dimensions can not all satisfy hypotheses of traditional theory analysis, which make its accurate analysis of the rigidity difficult. Here, based on finite element methods, the kinematics and mechanics principle of three typical flexible hinges is studied. Compared with results of traditional theory analysis, the error reasons are analyzed, and the influence of geometrical parameters on its rigidity is given.