During the manufacture of slabs with a veined effect a liquid or powder coloring agent is deposited on the surface of a thin layer of starting mixture by means of at least one dispensing device (40) and the resultant mixture is supplied, falling freely, from one end of an extractor belt (30) forming the bottom of a mixture metering/distributor unit, following which the mixture is transferred, falling freely, onto a temporary molding support (14). This results in the production of slabs provided with veining extending through the entire thickness of the slabs and also visible along the whole edge of the slab, even after it has been machined.