When a synthetic quartz glass substrate is prepared from a synthetic quartz glass block, (I) the block has a hydrogen molecule concentration of 5×1017-1×1019 molecules/cm3, (II) the substrate has a hydrogen molecule concentration of 5×1015-5×1017 molecules/cm3, (III) the substrate has an in-plane variation of its internal transmittance at 193.4 nm which is up to 0.2%, and (IV) the substrate has an internal transmittance of at least 99.6% at 193.4 nm. The synthetic quartz glass substrate has a high transmittance and a uniform transmittance distribution, and is adapted for use with excimer lasers, particularly ArF excimer lasers.