This paper presents an optimal design and the performance evaluation of two-axis nano positioning stage with round notched flexure hinges. A flexure hinge mechanism with round notched flexure hinges is to guide the linear motions of a moving plate in the nano positioning stage. A Min-Max algorithm is applied to the design of the flexure hinge mechanism for nano positioning stage. In the design process, the structure of the flexure hinge mechanism is fixed, then the radius of a round hole and the width of two round holes are chosen as design variables, and finally the do sign variables are calculated by the Min-Max algorithm. The machined flexure hinge mechanism, stack type PZTs for actuation and capacitance type displacement sensors for position measurement are assembled into the nano positioning stage. The experimental results of the manufactured nano positioning stage show the first modal resonance frequency of 197 Hz, the operating range of 40 um, and the resolution of 3 nm.