An apparatus for the sterilization of containers with a conveying device which conveys the containers along a pre-set conveying path, with at least one stressing device which acts upon the containers with radiation, for the purpose of the sterilization thereof, and with a screening device which screens off X-ray radiation which is formed in the context of the sterilization. The screening device has at least one outer wall which bounds the conveying path of the containers and which extends along the conveying path. The outer wall has at least one recess which forms a cavity which faces the conveying path of the containers in such a way that X-ray radiation formed during the sterilization can enter this cavity.