The invention relates to a steam generator with a distributor pipe arranged in a steam-generating space and having discharge openings. In this steam generator, the distributor pipe is fed from a water feed line which can be shut off, the water drops from the discharge openings of the distributor pipe onto an electrically heated evaporating area of the steam-generating space, and the generated steam flows out of the steam-generating space via a steam outlet. Simple assembly of the heating elements or simple replacement of the heating elements upon reaching the end of their useful life is achieved by the evaporating area being part of a solid storage block which can be heated up outside the steam-generating space by means of at least one panel heating element which is in heat-transfer contact.