Desirable wafer edge flatness was investigated to obtain optimum free-standing wafer edge shape for photolithography. In order to obtain the criteria of free-standing edge shape, we clarified the desirable post-chuck flatness at edge sites in advance. We investigated a desirable free-standing wafer edge, taking into consideration both the wafer and wafer holder shape. Firstly, to obtain a desirable post-chuck wafer edge shape, the vicinity of wafer edge after chucking was modeled, and SFQR was simulated. Secondly, a shape in the vicinity of free-standing edge shape was modeled, and the edge flatness after chucking was simulated. And finally, the simulated flatness was compared with the desirable post-chucked wafer edge shape, and we could obtain desirable free-standing wafer edge shape. Individual measurement of the free-standing back-side and front-side surfaces as well as the thickness of the edge position was found to be necessary for accurate estimation of the post-chuck edge shape.