A core is provided with a coating formed by an agglomerate obtained by hardening of a mixture comprising a granulated stone material, preferably of the type having a high hardness factor and light color, and a hardening resin, preferably an epoxy resin, for manufacturing a roller or cylinder of a non-porous external surface, the roller being used for the processing of materials and products. For the manufacture of the roller, a formwork having a cavity for housing a core is prepared so as to provide an interspace which is filled with the mixture, following which compacting of the mixture present in the interspace and then the resin hardening step are performed to obtain a non-porous agglomerate.