The invention relates to a process for the purification of fluoride-containing 65 to 95% strength waste sulfuric acid which contains water, organic impurities and fluoride. The impure sulfuric acid is introduced onto the top tray of a stripping column, in which this waste acid is heated and pre-concentrated. The heated acid then flows into a heating tank filled with boiling concentrated sulfuric acid. The sulfuric acid vapors escaping from this heating tank are condensed in the stripping column by the waste sulfuric acid flowing in counter-current. According to the invention, at least in the region of one tray of the stripping column, construction components which come into contact with acid vapors or liquid acid consist of acid-resistant plastic, at least on the surface.