UV-hardenable reaction resin compounds are irradiated in an applicator and immediately fed to an object that is to be covered. An initial, not activated reaction resin compound is irradiated after entering an input opening in a reactor having an irradiation space, a UV-radiation source and, optionally, a reflector. Immediately thereafter the activated compound is fed to an object to be coated or to an object to be surrounded, in an open casting mold or to a closed casting mold via the exit opening, optionally via a casting canal. The method and the apparatus are particularly well suited for covering semiconductor components and for encapsulating active and passive components as well as for cementing UV-impermeable fitting parts.