The process includes the introduction of a bi-component silicone resin (6) into the container (4), the placement of at least one solid cosmetic product (5) on said silicone resin (6) introduced in the container (4), and the polymerization of the resin (6) with consequent anchoring of the cosmetic product (5) to the container (4). The bi-component silicone resin is a modified polyvinyldimethylsiloxane-based resin consisting of two low viscosity elastomeric silicones, polyvinylmethylvinylsiloxanes and polymethylhydrogensiloxanes, suitably mixed. In particular, a RTV-GEL resin or an elastomeric RTV resin is used.