A synthetic quartz glass member for use in ArF excimer laser lithography comprising a high purity synthetic quartz glass and wherein layered structures, striae in three directions and internal strains are thermally and mechanically removed, the distribution of refractive index (Δn) in a plane orthogonal to the optical axis is 1×10−6 or less, the distribution of refractive index (Δn) in a plane parallel to the optical axis is 5×10−6 or less, the birefringence is 2 nm/cm or lower, the hydrogen molecule concentration is 2×1017 molecules/cm3 or higher, and the internal transmittance for wavelength at 193.4 nm is 99.8% or higher, wherein the synthetic quartz glass member shows an outer surface surrounding a bulk glass material, whereby there exists a Na concentration distribution such that the Na concentration is as high as 25 to 60 wt.-ppb at the outer surface and decreasing toward the bulk glass material, and whereby the synthetic quartz glass member was irradiated by ultraviolet rays at a wavelength of 260 nm or less and at an irradiation dose of at least 10 mW/cm2 for at least 48 hours.