A system for measuring ionizing radiation with a scintillator incorporates a first assembly of at least two rod-shaped scintillator elements, which can be optically coupled to one another via their opposed face ends. The first assembly of scintillator elements is coaxially enclosed by a second assembly of interconnectable sheath elements. According to the invention, one scintillator element (11), one sheath element (12) and two face-end window elements (131, 132) form a scintillator module (10) in each case, which is optically and mechanically connectable to additional scintillator modules. The individual scintillator elements can thus be produced as encapsulated scintillator modules by means of "suitable" sheath elements and window elements. This provides for a simple and reliable manipulation and assembly of the measuring assembly at the site of its application.