The device shields from X-radiation produced by electron bombardment of printed inks on a paper sheet in an apparatus including a press device, an electron bombardment device following the press device and a conveying device conveying the paper sheet from the press device through the electron bombardment device to the conveying device. To prevent smearing and double images on the paper sheet the device includes an upstream shielding duct device extending between the press device and the electron bombardment device through which the paper sheet is conveyed; a downstream shielding duct device extending between the electron bombardment device and the downstream conveying device through which the paper sheet is conveyed; a mechanism for contactless transport of the paper sheet from the press device, through the shielding duct devices and the electron bombardment device and to the conveying device; shielding components for shielding from X-radiation provided in press device; and shielding components for shielding against X-radiation provided in the downstream conveying device. Advantageously the upstream and downstream shielding duct devices extend into the press device and the conveying device respectively and the entrance of the upstream shielding duct device is adjacent and close to a contact surface of a press cylinder of the press device.