A synthetic quartz glass substrate is prepared by furnishing a synthetic quartz glass block, coating two opposite surfaces of the block with a liquid having a transmittance of at least 99.0%/mm at the wavelength of birefringence measurement, measuring a birefringence distribution on the block by letting light enter one coated surface and exit the other coated surface, and sorting the block to an acceptable group or unacceptable group, based on the measured birefringence distribution.