In the light of the disadvantages of the prior art technology, an object of the present invention is to provide a method for producing a synthetic 
quartz glass member for 
excimer lasers, which comprises, while suppressing the generation of reductive defects which impairs the resistance against 
laser radiations, incorporating a sufficient amount of 
hydrogen molecules capable of achieving a 
high resistance against 
laser radiation into the 
quartz glass, yet uniformly incorporating the 
hydrogen molecules to realize a flat distribution in refractive indices attributed to the distribution in the density of 
hydrogen molecules. It is also an object of the present invention to provide a synthetic 
quartz glass member for 
excimer lasers obtained by the production method above, which yields 
high resistance against 
laser radiations and homogeneity. The above problems have been overcome by a method for producing a synthetic quartz glass member for 
excimer lasers, which, in a method for producing a synthetic quartz glass member for 
excimer laser optics comprising a step of incorporating hydrogen molecules into a synthetic quartz glass body by 
heat treating the synthetic quartz glass body at a temperature of 600° C. or lower under an 
atmosphere in a 
pressure range of 1 atm or higher but lower than 150 atm and containing hydrogen, said method comprises varying the pressure of the gas containing hydrogen either continuously or stepwise in at least a part of the heat treatment.