In a quadrangular photomask blank substrate with a length on each side of at least 6 inches, which has a pair of strip-like regions that extend from 2 to 10 mm inside each of a pair of opposing sides along an outer periphery of a substrate top surface, with a 2 mm edge portion excluded at each end, each strip-like region is inclined downward toward the outer periphery of the substrate, and a difference between maximum and minimum values for height from a least squares plane for the strip-like region to the strip-like region is at most 0.5 μm. The substrate exhibits a good surface flatness at the time of wafer exposure.