A known method for producing synthetic quartz glass comprises the method steps: (a) forming a cylindrical SiO2 soot body having an inner portion and at least one free cylinder jacket surface surrounding the inner portion; (b) thermally drying the porous soot body; and (c) vitrifying the dried soot body with formation of the cylinder from synthetic quartz glass. Starting therefrom, to indicate a method which permits a particularly flat radial distribution in the inner portion of the cylinder, it is suggested according to the invention that the dried SiO2 soot body that is present after method step b) should be subjected to a homogenizing method prior to vitrification, the homogenizing method comprising the following steps: (I) heating the soot body to a consolidation temperature to form a sealing layer in the area of the at least one cylinder jacket, the sealing layer sealing the inner portion to the outside; (II) cooling the soot body from the consolidation temperature; and (III) annealing the soot body in the range of a homogenization temperature during a period of at least 5 hours so that the radial profile of the hydroxyl group concentration flattens in the inner portion.